714

Representation Theory andHarmonic Analysis on

Symmetric Spaces

AMS Special Session in Honor of Gestur Ólafsson’s 65thBirthday

Harmonic AnalysisJanuary 4, 2017

Atlanta, Georgia

Jens Gerlach ChristensenSusanna Dann

Matthew DawsonEditors

Representation Theory andHarmonic Analysis on

Symmetric Spaces

AMS Special Session in Honor of Gestur Ólafsson’s 65thBirthday

Harmonic AnalysisJanuary 4, 2017

Atlanta, Georgia

Jens Gerlach ChristensenSusanna Dann

Matthew DawsonEditors

714

Representation Theory andHarmonic Analysis on

Symmetric Spaces

AMS Special Session in Honor of Gestur Ólafsson’s 65thBirthday

Harmonic AnalysisJanuary 4, 2017

Atlanta, Georgia

Jens Gerlach ChristensenSusanna Dann

Matthew DawsonEditors

EDITORIAL COMMITTEE

Dennis DeTurck, Managing Editor

Michael Loss Kailash Misra Catherine Yan

2010 Mathematics Subject Classification. Primary 15A66, 17B40, 20C08, 22E46, 22E50,32L25, 32M15, 43A90, 53C35, 81R40.

Library of Congress Cataloging-in-Publication Data

Names: Christensen, Jens Gerlach, 1975- editor. | Dann, Susanna, 1977- editor. | Dawson,Matthew, 1990- editor.

Title: Representation theory and harmonic analysis on symmetric spaces : AMS special session

on harmonic analysis in honor of Gestur Olafsson’s 65th birthday, January 4, 2017, Atlanta,Georgia / Jens Gerlach Christensen, Susanna Dann, Matthew Dawson, editors.

Description: Providence, Rhode Island : American Mathematical Society, [2018] | Series: Con-temporary mathematics ; volume 714 | Includes bibliographical references.

Identifiers: LCCN 2018005036 | ISBN 9781470440701 (alk. paper)

Subjects: LCSH: Olafsson, Gestur. | Symmetric spaces–Congresses. | Harmonic analysis–Congresses. | Festschriften. | AMS: Linear and multilinear algebra; matrix theory – Basic linearalgebra – Clifford algebras, spinors. msc | Nonassociative rings and algebras – Lie algebras andLie superalgebras – Automorphisms, derivations, other operators. msc | Group theory and gen-eralizations – Representation theory of groups – Hecke algebras and their representations. msc |Topological groups, Lie groups – Lie groups – Semisimple Lie groups and their representations.msc | Topological groups, Lie groups – Lie groups – Representations of Lie and linear algebraicgroups over local fields. msc | Several complex variables and analytic spaces – Holomorphic fiberspaces – Twistor theory, double fibrations. msc | Several complex variables and analytic spaces– Complex spaces with a group of automorphisms – Hermitian symmetric spaces, bounded sym-metric domains, Jordan algebras. msc | Abstract harmonic analysis – Abstract harmonic analysis– Spherical functions. msc | Differential geometry – Global differential geometry – Symmetricspaces. msc | Quantum theory – Groups and algebras in quantum theory – Symmetry breaking.msc

Classification: LCC QA649 .R47 2018 | DDC 516.3/62–dc23 LC record available athttps://lccn.loc.gov/2018005036

Contemporary Mathematics ISSN: 0271-4132 (print); ISSN: 1098-3627 (online)

DOI: http://dx.doi.org/10.1090/conm/714

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10 9 8 7 6 5 4 3 2 1 23 22 21 20 19 18

Contents

Preface vii

List of Speakers ix

Gestur Olafsson’s contributions to Mathematics xiii

Schur Q-functions and the Capelli eigenvalue problem for the Lie superalgebraq(n)

Alexander Alldridge, Siddhartha Sahi, and Hadi Salmasian 1

Analysis of free products of the general linear groups GL2(Qp) and Heckealgebras H(GL2(Qp)) over primes p

Ilwoo Cho and Palle E. T. Jorgensen 23

Atomic decompositions of mixed norm Bergman spaces on tube type domainsJens Gerlach Christensen 77

C*-algebraic normalization and Godement-Jacquet factorsPierre Clare 87

Radial Toeplitz operators on the weighted Bergman spaces of Cartan domainsMatthew Dawson and Raul Quiroga-Barranco 97

A rational theory of Clebsch-Gordan coefficientsRobert W. Donley, Jr. and Won Geun Kim 115

Radon-John transforms and spherical harmonicsRicardo Estrada and Boris Rubin 131

Spherical functions on Riemannian symmetric spacesSigurdur Helgason 143

Schrodinger-type equations and unitary highest weight representations of themetaplectic group

Markus Hunziker, Mark R. Sepanski, and Ronald J. Stanke 157

Residue formula for regular symmetry breaking operatorsToshiyuki Kobayashi 175

On the geometry of standard subspacesKarl-Hermann Neeb 199

Pure spinors and a construction of the E∗-Lie algebrasMarcus J. Slupinski and Robert J. Stanton 225

v

vi CONTENTS

Representations on partially holomorphic cohomology spaces, revisitedJoseph A. Wolf 253

Preface

Dating back to the original work of Fourier on the solution to the heat equationusing trigonometric series and the subsequent work of 19th- and early 20-centurymathematicians to put it on a rigorous foundation, harmonic analysis has beenan active area of research whose fruitful connections to other branches of mathe-matics have steadily grown stronger and more numerous over time. This volume,for instance, features articles in the areas of integral geometry, complex analysis,operator algebras, Lie algebras, special functions, and differential operators. Thebreadth of contributions showcases the diversity of current research in harmonicanalysis and shows that it continues to be a vibrant and fruitful field of inquiry.

The connection between representation theory and harmonic analysis on sym-metric spaces is, in particular, emphasized by many of the articles in this volume.This relationship has a long history, including many classical and famous results byGelfand, Helgason, Harish-Chandra and others which have allowed, for instance,the development of a very precise description of the decomposition of the unitary,quasiregular representation associated to a Riemannian symmetric space G/K asa direct integral of so-called K-spherical representations of G with respect to aPlancherel measure given in terms of the beautiful c-function of Harish-Chandra.Several decades after these fundamental results, the role played by representationtheory in analysis on symmetric spaces continues to be successfully exploited, asexhibited by many of the articles we have collected here.

This volume grew out of an AMS Special Session at the Joint MathematicsMeeting in Atlanta, Georgia in January, 2017. This session was held in honor ofGestur Olafsson on his 65th birthday, and celebrated his many and wide-rangingcontributions to the area of harmonic analysis. The session drew experts fromaround the globe, and several have also contributed to this volume. Gestur Olafssonhas made important contributions to harmonic analysis on symmetric spaces, uni-tary representations of semisimple Lie groups, reflection positivity in quantum fieldtheory (including its connections with analysis on symmetric spaces), and wavelettheory, to name a few areas.

As students of Gestur, we are immensely grateful for the guidance and leader-ship he has shown us over the years. We have always found him to be exceptionallygenerous with his time and ideas, both as a mentor and as a collaborator. Withthis volume we wish to say both “thank you” and “congratulations” to our mentor.

We wish to thank the participants of the special session for making it such asuccess, as well as the contributors to this volume, which we hope will serve as amotivation and point of entry for young researchers, as well as provide valuableinformation for experts in this field. Thank you also to the many referees, withoutwhose valued opinions this would not have been possible. Last but not least, we

vii

viii PREFACE

thank the American Mathematical Society for letting us organize the special session,as well as Chris Thivierge for her help during the preparation of this volume.

List of Speakers

AMS Special Session on Harmonic Analysis(In Honor of Gestur Olafsson’s 65th Birthday) I & II

Joint Mathematics MeetingsAtlanta, GA

January 4, 2017

Pierre Clare (Dartmouth College): Geometric pictures of intertwining oper-ators.

Matthew Dawson (CIMAT, Mexico): Principal series representations ofdirect-limit groups.

Fulton B Gonzalez (Tufts University): Surjectivity of Mean Value Opera-tors on Noncompact Symmetric Spaces.

Benjamin Harris (Bard College at Simon’s Rock): Vogan-ZuckermanCharacters and Semisimple Coadjoint Orbits.

Markus Hunziker (Baylor University): The Tricomi equation and comple-mentary series representations of SL(2,R).

Toshiyuki Kobayashi (The University of Tokyo): Conformally CovariantSymmetry Breaking Operators on Differential Forms and Some Applica-tions.

Sergii Myroshnychenko (Kent State University): On polytopes with con-gruent projections or sections.

Angela Pasquale (Universite de Lorraine): Radial parts of differential op-erators and a one-parameter family of hypergeometric functions of typeBC.

Raul Quiroga-Barranco (CIMAT, Mexico): Multiplicity-free restrictions ofholomorphic discrete series and Toeplitz operators.

Boris Rubin (Louisiana State University): New Inversion Formulas for theHorospherical Transform.

Siddhartha Sahi (Rutgers University): Macdonald hypergeometric funct-ions.

Henrik Schlichtkrull (University of Copenhagen, Denmark): Realspherical spaces and their classification.

Robert J. Stanton (Ohio State University): Duality of geometries on flagmanifolds associated to maximal parabolic subgroups in split G2.

Bent Ørsted (Aarhus University, Denmark): Homomorphisms betweenVerma modules and small representations.

ix

Participants

inth

esp

ecialsession

From

left

toright:

Rau

lQuiroga-B

arranco,PierreClare,BorisRubin,Mark

Sepanski,MarkusHunziker,

AngelaPasquale,Susanna

Dann,ToshiyukiKobayashi,Matthew

Daw

son,GesturOlafsson,SergiiMyroshnychenko,SiddhartaSahi,HenrikSchlichtkrull,Ben

Harris,BentØrsted,RobertDonley,

RobertStanton.JensChristensen,FultonGonzalez

Photo

courtesyof

GesturOlafsson

xi

Gestur Olafsson’s contributions to Mathematics

Books

(1) J. Hilgert and G. Olafsson: Causal Symmetric Spaces, Geometry andHarmonic Analysis. Perspectives in Mathematics 18, Academic Press,1996

(2) R. Fabec and G. Olafsson: Non-Commutative Harmonic Analysis. Drex-ville Publishing, 2014.

(3) K.-H. Neeb and G. Olafsson, Reflection Positivity: A Representation The-oretic Perspective. To appear in Springer Briefs in Math. Physics., August2018.

Refereed articles and refereed chapters in books and specialvolumes

(1) Die Langlands-Parameter fur die Flensted-Jensensche fundamentaleReihe. Math. Scand. 55 (1984) 229-244.

(2) Fourier and Poisson transformation associated to a semisimple symmetricspace. Invent. Math. 90 (1987) 605-629.

(3) (with B. Ørsted) The holomorphic discrete series for affine symmetricspaces I. Journal of Funct. Anal. 81 (1988), 126-159.

(4) (Habilitation) Causal symmetric spaces. Mathematica Gottingensis 15(1990)

(5) Symmetric Spaces of Hermitian Type. Differential Geometry and Appli-cations 1 (1991), 195-233

(6) (with B. Ørsted) The holomorphic discrete series of an affine symmetricspace and representations with reproducing kernels, Trans. Amer. Math.Soc. 326 (1991), 385-405.

(7) (with J. Hilgert and B. Ørsted) Hardy Spaces on Affine Symmetric Spaces.J. reine und angew. Math. 415 (1991), 189-218

(8) (with T. P. Branson) Equipartition of Energy for Waves in SymmetricSpaces. J. Funct. Anal. 97 (1991), 403-416.

(9) (with H. Schlichtkrull) Wave propagation on Riemannian symmetric space.J. Funct. Anal. 107 (1992) 270-278.

(10) (with B. Ørsted) Analytic continuation of Flensted-Jensen Representa-tion. Manuscripta Math. 74 (1992), 5-23.

(11) (with J. Hilgert) Analytic extensions of representations, the solvable case.Jap. Journ. Math. 18 (1993) 213-290

(12) (with T. Branson and H. Schlichtkrull): A bundle valued Radon trans-form, with applications to invariant wave equations. Quart. J. Math.Oxford 45 (1994) 429-461.

xiii

xiv GESTUR OLAFSSON’S CONTRIBUTIONS TO MATHEMATICS

(13) (with J. Faraut and J. Hilgert): Spherical functions on ordered symmetricspaces. Ann. Inst. Fourier 44 (1994), 927-966

(14) (with J. Faraut): Causal Semisimple Symmetric Spaces: The Geometryand Harmonic Analysis. In: Ed. Hofmann, Lawson, Vinberg: “Semi-groups in Algebra, Geometry and Analysis”, 3-32, 1995.

(15) (with T. Branson and H. Schlichtkrull): Huyghens’ Principle in Riemann-ian Symmetric Spaces. Math. Ann. 301, 445-462 (1995)

(16) (with T. Branson and B. Ørsted): Spectrum Generating Operators, andIntertwining Operators for Representations Induced from a maximal Par-abolic Subgroup. J. Funct. Anal. 135 (1996) 163-205.

(17) (with B. Ørsted) Generalization of the Bargmann Transform. Proceedingsof a “Workshop on Lie Theory and its Applications in Physics” Clausthal,August 1995. Ed. Dobrev, Dobner, Hilgert. World Scientific, 1996

(18) (with T. Branson): Helmholtz Operators and Symmetric Space Duality.Invent. Math. 129, 63-74 (1997).

(19) (with B. Krotz and K-H. Neeb) Spherical Representations and MixedSymmetric Spaces. Representation Theory 1, 424-461 (1997).

(20) Open Problems in Harmonic Analysis on Causal Symmetric Spaces. p.249-270. In: Positivity in Lie Theory; Open Problems. Ed. J. Hilgert, J.D. Lawson, K-H. Neeb, E. B. Vinberg, De Gruyter 1998.

(21) (with P. Jorgensen) Unitary Representations of Lie Groups with ReflectionSymmetry. J. Funct. Anal. 158 (1998) 26-88 (1998).

(22) (With A. G. Helminck, J. Hilgert, A. Neumann) A Conjugacy Theoremfor Symmetric Spaces. Mathematische Annalen 313 (1999), 785-791.

(23) (with T. Branson) Asymptotics of the D’Alembertian with Potential on aPseudo-Riemannian Manifold. Proceedings of the AMS 127 (1999), 1339-1345.

(24) (With B. Ørsted) Causal Compactification and Hardy Spaces. Trans.AMS 351 (1999), 3771-3792.

(25) (with P. Jorgensen) Osterwalder-Schrader Axioms - Wightman Axioms.Encyclopaedia of Mathematics, Supplement II Kluwer, Jan. 2000.

(26) (with P. Jorgensen) Unitary representations and Osterwalder-SchraderDuality. Ed. R. S. Doran, V. S. Varadarajan: The Mathematical Legacyof Harish-Chandra: A Celebration of Representation Theory and Har-monic Analysis, PSPM, AM, 2000.

(27) (with A. Neumann) Minimal and Maximal Semigroups Related to CausalSymmetric Spaces. Semigroup Forum 61 (2000) 57–85.

(28) Analytic Continuation in Representation Theory and Harmonic Analysis.In: Global Analysis and Harmonic Analysis, ed. J. P. Bourguignon, T.Branson, and O. Hijazi. Seminares et Congr, vol 4, (2000), 201–233. Pub.:The French Math. Soc.

(29) (with N. Andersen) A Paley-Wiener Theorem for the Spherical LaplaceTransform on Causal Symmetric Spaces of Rank One. Proceedings of theAMS. 129 (2001), 173–179.

(30) (with A. Pasquale) On the meromorphic extension of the spherical func-tions on noncompactly causal symmetric spaces. J. Funct. Analysis 181(2001), 346–401.

GESTUR OLAFSSON’S CONTRIBUTIONS TO MATHEMATICS xv

(31) (with B. Krotz and K-H. Neeb) Spherical Functions on Mixed SymmetricSpaces. Representation Theory, 5 (2001), 43-92.

(32) (with F. Betten) Causal Compactification and Hardy Spaces for Spacesof Hermitian Type. Pacific J. Math. 200 (2001), 273–312.

(33) (with A. Pasquale) Regularity properties of generalized Harish-Chandraexpansions. In: A. Strasburger et al. (eds.), Geometry and analysis onfinite- and infinite-dimensional Lie groups , Banach Center Publications55 (2002), 335-348. Banach Center Publications, 2002.

(34) (with M. Davidson and G. Zhang) Laguerre polynomials, restriction prin-ciple, and holomorphic representations of SL(2,R). Acta ApplicandaeMathematicae 71 (3) (2002) 261–277.

(35) (with B. Krotz) The c-function for non-compactly causal symmetric spa-ces. Invent. Math. 149 (2002) 3, 647–659.

(36) (with R. Fabec) The continuous Wavelet transform and symmetric spaces.Acta Applicandae Mathematicae 87(1) (2003), 261–277.

(37) (with S. Gindikin and B. Krotz) Hardy spaces for non-compactly causalsymmetric spaces and the most continuous spectrum. Math. Ann. 327(2003), 25–66.

(38) (with N. B. Andersen and H. Schlichtkrull) On the inversion of the Laplaceand Abel Transforms for causal symmetric spaces. Forum Math. 15(2003), 679–699.

(39) (with M. Davidson and G. Zhang) Laplace and Segal-Bargmann trans-forms on Hermitian symmetric spaces and orthogonal polynomials. J.Funct. Anal. 204 (2003), 157–195.

(40) (with Mark Davidson) Differential recursion relations for Laguerre func-tions on Hermitian matrices. Integral Transforms and Special Functions14 (2003) 469–484.

(41) (with B. Krotz) The c-function for non-compactly causal symmetric spacesand its relations to harmonic analysis and representation theory Ed. S.G.Gindikin, Lie groups and symmetric spaces, In memory of F.I. Karpele-vich. AMS Translations 210, 171–194 (2003).

(42) (with M. Davidson) The Generalized Segal-Bargmann transform and Spe-cial Functions Acta Applicandae Mathematicae, 81 (2004), 29–50.

(43) (with A. Pasquale) Paley-Wiener theorems for the Θ-spherical transform:An overview. Acta Applicandae Mathematicae 81 (2004), 275–309.

(44) (with D. Speegle) Wavelets, wavelet sets, and linear actions on Rn, Con-temporary Mathematics (AMS) 345, Wavelets, Frames and Operator The-ory, Eds: C. Heil, P. Jorgensen, D. Larson, 2004, 253–281.

(45) (with A. Pasquale) A Paley-Wiener Theorem for the Θ-spherical Trans-form: The Even Multiplicity case. Journal de mathematiques pures etappliquees 83 (2004), 811–954.

(46) (with S. Gindikin and B. Krotz) Erratum: Holomorphic H-spherical dis-tribution vectors in principal series representations. Inventiones Mathe-maticae 158 (2004), 683-684.

(47) (with S. Gindikin and B. Krotz) Holomorphic H-spherical distributionvectors in principal series representations. Inventiones Mathematicae 158(2004), 643–682.

xvi GESTUR OLAFSSON’S CONTRIBUTIONS TO MATHEMATICS

(48) (with B. Krotz and R. Stanton) The image of the heat kernel transformon Riemannian symmetric spaces of the noncompact type. 22 (2005),1307–1329 International Mathematics Research Notices.

(49) Continuous action of Lie groups on Rn and frames. International Journalof Wavelets, Multiresolution and Information Processing 3 No. 2 (2005),211–235.

(50) (with T. Branson and A. Pasquale) The Paley-Wiener Theorem for theJacobi Transform and the Local Huygens’ Principle for Root Systems withEven Multiplicities. Indagationes 16 (2005), 429–442. Special volume ofIndagationes in honor of G. van Dijk.

(51) (with T. Branson and A. Pasquale) The Paley-Wiener Theorem and thelocal Huygens’ principle for compact symmetric spaces. Indagationes 16(2005), 393–428. Special volume of Indagationes in honor of G. van Dijk.

(52) (with M. Dobrescu) Wavelets without groups. Contemp. Math. 405(2006), 27–40.

(53) (with A. Pasquale) Support properties and Holmgren’s uniqueness the-orem for differential operators with hyperplane singularities. J. Funct.Anal. 239 (2006), 21–43.

(54) (with S. Gindikin and B. Krotz) Horospherical model for the holomor-phic discrete series and the horospherical Cauchy transform. CompositioMathematica 142 (2006) 983–1008.

(55) (with R. Fabec and A. Sengupta) Fock spaces corresponding to positivedefinite linear transformations. Math. Scand 98 (2006) 262–282.

(56) (with M. Davidson and M. Aristidou) Differential Recursion Relations forLaguerre Functions on Symmetric Cones. Bull. Sci. math. 130 (2006),346–263.

(57) (with E. Ournycheva, and B. Rubin) Higher-ranked wavelet transforms,ridgelets transforms, and Radon Transform on the space of matrices. Ap-plied and Computational Harmonic Analysis 21 (2006) 182–203.

(58) (with S. Gindikin and B. Krotz) Holomorophic horospherical transformon non-compactly causal spaces. IMRN 2006 (2006), 1–47.

(59) (with S. Zheng) Function spaces associated with Schrodinger Operators:The Poschl-Teller Potential. J. Fourier Anal. and Appl. 12 (2006), 653–674

(60) (with M. Aristidou and M. Davidson) Laguerre functions on symmetriccones and recursion relations in the real case. J. Computational and Ap-plied Mathematics., 199 (2007), 95–112.

(61) (with H. Schlichtkrull) The Segal-Bargmann transform for the heat equa-tion associated with root systems. Adv. Math. 208 (1) (2007), 422–437.

(62) (with H. Schlichtkrull) Representation theory, Radon transform and theheat equation on a Riemannian symmetric space. Group Representa-tions, Ergodic Theory, and Mathematical Physics; A Tribute to GeorgeW. Mackey. In: Contemp. Math., 449 (2008), 315–344.

(63) (with H. Schlichtkrull) A local Paley-Wiener theorem for compact sym-metric spaces. Adv. Math. 218 (2008), no. 1, 202–215.

(64) (with M. Dobrescu) Coxeter groups, wavelets, multiresolution and sam-pling. In Frames and operator theory in analysis and signal processing,119–135, Contemp. Math., 451, Amer. Math. Soc., Providence, RI, 2008.

GESTUR OLAFSSON’S CONTRIBUTIONS TO MATHEMATICS xvii

(65) (with S. Zheng) Harmonic Analysis Related to Schrodinger Operators.Contemporary Math. 464 (2008), 213–230.

(66) (with B. Rubin) Invariant functions on Grassmanians. Contemporarymath. 464 (2008), 201–212.

(67) (with J. G. Christensen) Examples of coorbit spaces for dual pairs. ActaAppl. Math. 107 (2009), 25–48.

(68) (with D. Larson, and P. Massopust) Three-way tiling sets in two dimen-sions. Acta Appl. Math. 108 (2009), no. 3, 529–546.

(69) (with H. Schlichtkrull) Fourier Series on Compact Symmetric Spaces: K-Finite Functions of Small Support. Journal of Fourier Anal. and Appl.16 (2010), 609–628.

(70) (with J. G. Christensen) Coorbit spaces for dual pairs. Applied and Com-putational Harmonic Analysis 31 (2011) 303–324.

(71) (with J. Wolf) Extension of Symmetric Spaces and Restriction of WeylGroups and Invariant Polynomials. Contemporary Math. 544, 85–100.

(72) (with S. Dann) Paley-Wiener Theorems with respect to the spectral pa-rameter. Contemporary Math. 544 (2011), 55–84.

(73) (with H. Schlichtkrull) Fourier Transform of Spherical Distributions onCompact Symmetric Spaces. Mathematica Scandinavica 190 (2011), 93–113.

(74) (with A. Pasquale) The Cosλ and Sinλ transforms as intertwining opera-tors between generalized principal series representations of SL(n+ 1,K).Advances in Mathematics 229 (2012), 267–293.

(75) (with A. Pasquale) Ramanujan’s Master Theorem for Riemannian sym-metric spaces. Journal of Functional Analysis, 262 (2012) 4851–4890.

(76) (with J. Christensen) and A. Mayeli) Coorbit description and atomic de-composition of Besov spaces. Numer. Funct. Anal. Optim. 33 (2012),no. 7–9, 847–871.

(77) (with M. Dawson and J. Wolf) Direct Systems of Spherical Functions andRepresentations, Journal of Lie Theory 23 (2013), 711–729.

(78) (with A. Pasquale and B. Rubin) Analytic and Group-Theoretic Aspectsof the Cosine Transform.In: Eds: E. T. Quinto, F. Gonzalez, J. Chris-tensen, Geometric Analysis and Integral Geometry, Contemporary Math.598, 167–188, Amer. Math. Soc., Providence, RI, 2013.

(79) (with R. Stanton) On the life and work of S. Helgason. In: Eds: E.T. Quinto, F. Gonzalez, J. Christensen, Geometric Analysis and IntegralGeometry, Contemporary Math. 598, (2013) p. 21–42,

(80) (with K. Wiboonton) The Segal-Bargmann transform on compact sym-metric spaces and their direct limits. In (Eds. A. Hucleberry, I. Penkov,G. Zuckerman) Lie Groups: Structure, Actions, and Representations. Inhonor of Joseph A. Wolf on the Occasion of his 75th Birthday. 225–253,Progr. Math., 306, Birkhauser/Springer, New York, 2013.

(81) (with J. Christensen) Sampling in Spaces of Bandlimited Functions onCommutative Spaces. In: Eds: T. D.Andrews, R. Balan, J. J. Benedetto,W. Czaja, K. A. Okoudjou. Excursion in Harmonic Analysis, Volume 1,135–69, Appl. Numer. Harmon. Anal., Birkhauser/Springer, New York,2013.

xviii GESTUR OLAFSSON’S CONTRIBUTIONS TO MATHEMATICS

(82) (with B. Harris and H. He) The continuous spectrum in discrete seriesbranching laws. International Journal of Mathematics 34 (2013).

(83) (with A. Pasquale) Ramanujan’s master theorem for the hypergeometricFourier transform associated with root systems. J. Fourier Anal. Appl.,19 (2013), 1150–1183.

(84) (with J. Wolf) The Paley-Wiener theorem and limits of symmetric spaces.J. Geometric Anal.. 24 (2014), 1-31.

(85) (with K.-H. Neeb) Reflection positivity and conformal symmetry. Journalof Functional Analysis. 266 (2014), 2174–2224.

(86) (with J. Hilgert) The Radon transform and its dual for limits of symmetricspaces. In: Developments and Retrospectives in Lie Theory, Springer,2014, 77–111.

(87) (with M. Dawson and R. Quiroga-Barranco) Commuting Toeplitz opera-tors on bounded symmetric domains and multiplicity-free restrictions ofholomorphic discrete series. J. Funct. Anal. 268 (2015), 1711–1732.

(88) (with S. Merigon and K-H. Neeb) Integrability of unitary representationson reproducing kernel spaces, Representation Theory, 19 (2015), 24–55.

(89) (with K-H. Neeb) Reflection positive one-parameter groups and dilations.Complex Anal. Oper. Theory 9 (2015), 653–721.

(90) (with K.-H. Neeb) Reflection positivity for the circle group. J. of Physics:Conference Series 597 (2015), 16 pages.

(91) (with V. Ho) An application of hypergeometric shift operators to the χ-spherical Fourier transform. Contemporary Math. 650 (2015), 143–155.

(92) (with M. Dawson) A Survey of Amenability Theory for Direct-LimitGroups. Contemporary Math. 650 (2015), 89–109

(93) (with B. Harris and H. He) Wave Front Sets of Reductive Lie GroupRepresentations. Duke Math. J. 165 (2016), 793–846.

(94) (with P. E. T. Jorgensen and K.-H. Neeb) Reflection positive stochasticprocesses indexed by Lie groups. SIGMA 12 (2016) 49 pages.

(95) (with J. Christensen and K. Grochenig) New atomic decompositions forBergman spaces on the unit ball. Indiana Univ. Math. J 66 (2017),205–235.

(96) (with M. Dawson) Conical representations for direct limits of symmetricspaces. Mathematische Zeitschrift, 286 (2017), 1375–1419.

(97) J. Frahm, G. Olafsson, and B. Ørated, The Berlin form on symmetric R-spaces and reflection positivity. Banach Center Publications 113 (2017),134–168.

(98) K.-H. Neeb and G. Olafsson, Antiunitary representations and modulartheory. Banach Center Publications 113 (2017), 291–362.

(99) G. Olafsson and R. Quiroga-Barranco, On low-dimensional manifolds withisometric U(p, q)-actions. Asian Journal of Mathematics 21 (2017), 87-907.

(100) P. Jorgensen, K-H. Neeb, and G. Olafsson, Reflection positivity on realintervals. Semigroup Forum, 96 (2018), 31–48.

(101) V. Ho and G. Olafsson, Paley-Wiener Theorem for Line Bundles overCompact Symmetric Spaces and New Estimates for the Heckman-OpdamHypergeometric Functions. Mathematische Nachrichten (2018), 25 pages.eprint = https://onlinelibrary.wiley.com/doi/pdf/10.1002/mana.201600148

GESTUR OLAFSSON’S CONTRIBUTIONS TO MATHEMATICS xix

Book reviews

(1) Lie Groups, Convex Cones and Semigroups, by J. Hilgert, K.H. Hofmannand J.D.Lawson. Oxford Univ. Press. 1989. Jahresbericht der DMV 95,(1992), 5-8

(2) Holomorphy and Convexity in Lie Theory by K.-H. Neeb, De GruyterExpositions in Mathematics, 8, Berlin, New York, 2000 Jahresbericht derDMV 104 (2002)

(3) Analysis and Probability; Wavelets, Signals, Fractals by P. E. T. Jor-gensen. Graduate Text in Mathematics, Springer, 2006. Journal of Ap-proximation Theory, 162 (2010), 233–236.

(4) Homogeneous spaces and equivariant embeddings by D. A. Timashev. En-cylopaedia of Mathematical Sciences 138, Springer, 2011. In: Bulletin ofthe AMS 51 (2014), 349–359.

Non refereed chapters in books, conference proceedings andother publications

(1) Several publications in Mathematica Gottingensis, publication of the Son-derforschungsbereich Geometry and Analysis at the University of Gottin-gen and material posted on my webpage.

(2) Ph.D. Thesis, Die Langlands-Klassifizierung, unitare Darstellungen unddie Flensted-Jensensche fundamentale Reihe. Gottingen, 1982.

(3) (with B. Ørsted) Is there an orbit method for affine symmetric spaces?In: The Orbit Method in Representation Theory, Proceedings of a Con-ference held in Copenhagen August to September 1988, Ed. M. Duflo,N.V. Pedersen, M. Vergne. Birkhauser, 1990.

(4) Unitary Representations with Reflection Symmetry. In: Proceedings ofan International Workshop on Lie Theory and its applications in physics.Ed. H-D. Dobner, V. K. Dobrev, J. Hilgert. World Scientific, 1999

(5) The c-function for symmetric spaces. A Contribution in Proceedings ofan International Workshop on Lie Theory and its applications in physics.Ed. H-D. Dobner, V. K. Dobrev, J. Hilgert. World Scientific, 2001

(6) Groups, Wavelets, and Function Spaces. In: Mathematisches Forschungs-institut Oberwolfach Report No. 10/2004, Mini-Workshop: Wavelets andFrames, February 15th-February 21st, 2004, Oberwolfach, 2004, 33–36

(7) (with H. Feichtinger, P. Jorgensen and D. Larson) Introduction to Math-ematisches Forschungsinstitut Oberwolfach Report No. 10/2004, Mini-Workshop: Wavelets and Frames, February 15th-February 21st, 2004,Oberwolfach, 2004, 3–5

(8) (with T. Quinto) Introduction. In: Ed. G. Olafsson and T. Quinto: TheRadon Transform, Inverse Problems, and Tomography. Proceedings ofSymposia in Applied Mathematics. AMS.

(9) (with E, Grinberg, P. Jorgensen, D. Larson, P. Massopust, T. Quinto, B.Rubin) Preface. In: Radon Transforms, Geometry, and Wavelets. Con-

temporary Mathematics 464, vii–ix,AMS, 2008, Chief Editor: G. Olafsson,editors E, Grinberg, P. Jorgensen, D. Larson, P. Massopust, T. Quinto,B. Rubin.

xx GESTUR OLAFSSON’S CONTRIBUTIONS TO MATHEMATICS

(10) Fourier-greining a vıxlnum grupum. Verpill 2009, 34–36. (Verpill is ajournal for students in mathematics and physics at the University of Ice-land. The English translation of the title is: Fourier analysis on Abeliangroups.)

(11) (with H. Schlichtkrull) Preface to The Selected Works of Surður Helgason,

ix–x, AMS, 2009. Editors: G. Olafsson and H. Schlichtkrull.(12) (with P. G. Casazza, P.E.T. Jorgensen, K.A. Kornelson, G. Kutyniok,

D.R. Larson, P. Massopust, J.A. Packer, S. Silvestrov and Q. Sun) Prefaseto a special volume of Numerical Functional Analysis and Optimization33 (2012), 705–707.

(13) (with J. Christensen and S. D. Casey) Sampling, amenability and theKunze-Stein phenomenon. IEEE Xplore-2015, International Conferenceon Sampling Theory and Applications (SampTA 2015) 68–72

Graduate Students

(1) Co-advisor, main advisor Prof. H. Holdgrun. H. Thorleifsson (Gottingen,1987): Die Langlandsparameter der Leiterdarstellung von U(p, q) (TheLanglands parameters of the Ladder representation of U(p, q)).

(2) Co-advisor, main advisor Prof. H. Holdgrun. J. Kochmann (Gottingen,1992): Vertauschungsoperatoren zur holomorphen diskreten Reihe speziel-ler symmetrischer Raume (Intertwining operators for holomorphic dis-crete series for special symmetric spaces).

(3) Co-advisor, main advisor Prof. H. Holdgrun. F. Betten (Gottingen, 1996):Kausale Kompaktifizierung kompakt kausaler Raume (Causal compactifi-cation of compactly causal spaces).

(4) T. Johansen (Louisiana State University, 2004): Orbit Structure on theSilov Boundary of a Tube Domain and the Plancherel Decomposition ofa Causally Compact Symmetric Space, with Emphasis on the Rank OneCase.

(5) I. Hossain (MS with concentration in Applications): Query by Image Con-tent Using Wavelets and Gibbs-Markov Random Fields.

(6) M. Dobrescu (Louisiana State University, 2005): Wavelet Sets with andwithout Groups and Multiresolution Analysis.

(7) M. Aristidou (Louisiana State University, 2005): Laguerre Functions As-sociated to Euclidean Jordan Algebras.

(8) K. Wiboonton (Louisiana State University, 2009): The Segal-BargmannTransform on Inductive Limits of Compact Symmetric Spaces.

(9) J. Christensen (Louisiana State University, 2009): Function Spaces, Wave-lets and Representation Theory.

(10) S. Dann (Louisiana State University, 2011): Paley-Wiener Theorems withRespect to the Spectral Parameter.

(11) V. Ho (Louisiana State University, 2012): Paley-Wiener Theorem for LineBundles over Compact Symmetric Spaces.

(12) M. Dawson (Louisiana State University, 2014): Conical Representationsfor direct limits of Riemannian Symmetric Spaces.

(13) C. A. Cross (Louisiana State University, 2015):Partial Cosine-Funk Trans-forms at Poles of the Cosine-λ Transform on Grassmann Manifolds.

GESTUR OLAFSSON’S CONTRIBUTIONS TO MATHEMATICS xxi

(14) A. Darweesh (Louisiana State University, 2015): Wavelets, Coorbit The-ory, and Projective Representation. Co-advisor Jens G. Christensen.

(15) M. Hayajneh (Louisiana State University, 2016): Twisted Reflection Pos-itivity.

Postdoctoral Scholars

(1) Andreas Neumann (Lousiana State University, 1998–2000)(2) Shijun Zheng (Lousiana State University, 2003–2005)(3) Benjamin Harris (Lousiana State University, 2011–2014)(4) Eli Vanney Roblero-Mendez (Lousiana State University, 2014)(5) Stephane Merigon (Lousiana State University, 2014)

Selected Published Titles in This Series

714 Jens Gerlach Christensen, Susanna Dann, and Matthew Dawson, Editors,Representation Theory and Harmonic Analysis on Symmetric Spaces, 2018

708 Christian Ausoni, Kathryn Hess, Brenda Johnson, Ieke Moerdijk, and JeromeScherer, Editors, An Alpine Bouquet of Algebraic Topology, 2018

707 Nitya Kitchloo, Mona Merling, Jack Morava, Emily Riehl, and W. StephenWilson, Editors, New Directions in Homotopy Theory, 2018

706 Yeonhyang Kim, Sivaram K. Narayan, Gabriel Picioroaga, and Eric S. Weber,Editors, Frames and Harmonic Analysis, 2018

705 Graham J. Leuschke, Frauke Bleher, Ralf Schiffler, and Dan Zacharia, Editors,Representations of Algebras, 2018

704 Alain Escassut, Cristina Perez-Garcia, and Khodr Shamseddine, Editors,Advances in Ultrametric Analysis, 2018

703 Andreas Malmendier and Tony Shaska, Editors, Higher Genus Curves inMathematical Physics and Arithmetic Geometry, 2018

702 Mark Grant, Gregory Lupton, and Lucile Vandembroucq, Editors, TopologicalComplexity and Related Topics, 2018

701 Joan-Carles Lario and V. Kumar Murty, Editors, Number Theory Related toModular Curves, 2018

700 Alexandre Girouard, Dmitry Jakobson, Michael Levitin, Nilima Nigam, IosifPolterovich, and Frederic Rochon, Editors, Geometric and Computational SpectralTheory, 2017

699 Mark L. Agranovsky, Matania Ben-Artzi, Catherine Beneteau, Lavi Karp,Dmitry Khavinson, Simeon Reich, David Shoikhet, Gilbert Weinstein,and Lawrence Zalcman, Editors, Complex Analysis and Dynamical Systems VII, 2017

698 Alexander M. Blokh, Leonid A. Bunimovich, Paul H. Jung, Lex G.Oversteegen, and Yakov G. Sinai, Editors, Dynamical Systems, Ergodic Theory, andProbability: in Memory of Kolya Chernov, 2017

697 Fabrizio Broglia, Francoise Delon, Max Dickmann, Danielle Gondard-Cozette,and Victoria Ann Powers, Editors, Ordered Algebraic Structures and Related Topics,2017

696 Ara S. Basmajian, Yair N. Minsky, and Alan W. Reid, Editors, In the Traditionof Ahlfors–Bers, VII, 2017

695 Katrina Barron, Elizabeth Jurisich, Antun Milas, and Kailash Misra, Editors,Lie Algebras, Vertex Operator Algebras, and Related Topics, 2017

694 Manjul Bhargava, Robert Guralnick, Gerhard Hiss, Klaus Lux, and Pham HuuTiep, Editors, Finite Simple Groups: Thirty Years of the Atlas and Beyond, 2017

693 Michael Cwikel and Mario Milman, Editors, Functional Analysis, HarmonicAnalysis, and Image Processing, 2017

692 Anatole Katok, Yakov Pesin, and Federico Rodriguez Hertz, Editors, ModernTheory of Dynamical Systems, 2017

691 Farrell Brumley, Maria Paula Gomez Aparicio, and Alberto Mınguez, Editors,Around Langlands Correspondences, 2017

690 Andres Eduardo Caicedo, James Cummings, Peter Koellner, and Paul B.Larson, Editors, Foundations of Mathematics, 2017

689 Erica Flapan, Allison Henrich, Aaron Kaestner, and Sam Nelson, Editors,Knots, Links, Spatial Graphs, and Algebraic Invariants, 2017

688 Jeffrey Bergen, Stefan Catoiu, and William Chin, Editors, Groups, Rings, GroupRings, and Hopf Algebras, 2017

For a complete list of titles in this series, visit theAMS Bookstore at www.ams.org/bookstore/conmseries/.

This volume contains the proceedings of the AMS Special Session on Harmonic Analysis,

in honor of Gestur Olafsson’s 65th birthday, held on January 4, 2017, in Atlanta, Georgia.

The articles in this volume provide fresh perspectives on many different directions

within harmonic analysis, highlighting the connections between harmonic analysis and the

areas of integral geometry, complex analysis, operator algebras, Lie algebras, special func-

tions, and differential operators. The breadth of contributions highlights the diversity of

current research in harmonic analysis and shows that it continues to be a vibrant and fruit-

ful field of inquiry.

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