Commutative and Noncommutative Harmonic Analysis and Applications: AMS Special Session in Memory of Daryl Geller on Wavelet and Frame Theoretic ... Septembe

218 Pages·2013·1.93 MB·English

by  Azita Mayeli

603
Commutative and
Noncommutative Harmonic
Analysis and Applications
AMS Special Session in Memory of Daryl Geller on
Wavelet and Frame Theoretic Methods in Harmonic
Analysis and Partial Differential Equations
September 22-23, 2012
Rochester Institute of Technology, Rochester, NY
Azita Mayeli
Alex Iosevich
Palle E. T. Jorgensen
Gestur Ólafsson
Editors
AmericanMathematicalSociety
Commutative and
Noncommutative Harmonic
Analysis and Applications
AMS Special Session in Memory of Daryl Geller on
Wavelet and Frame Theoretic Methods in Harmonic
Analysis and Partial Differential Equations
September 22-23, 2012
Rochester Institute of Technology, Rochester, NY
Azita Mayeli
Alex Iosevich
Palle E. T. Jorgensen
Gestur Ólafsson
Editors

603
Commutative and
Noncommutative Harmonic
Analysis and Applications
AMS Special Session in Memory of Daryl Geller on
Wavelet and Frame Theoretic Methods in Harmonic
Analysis and Partial Differential Equations
September 22-23, 2012
Rochester Institute of Technology, Rochester, NY
Azita Mayeli
Alex Iosevich
Palle E. T. Jorgensen
Gestur Ólafsson
Editors
AmericanMathematicalSociety
Providence,RhodeIsland
EDITORIAL COMMITTEE
Dennis DeTurck, Managing Editor
Michael Loss Kailash Misra Martin J. Strauss
2010 Mathematics Subject Classification. Primary 41-xx, 42-xx, 43-xx, 46-xx, 47-xx .
Library of Congress Cataloging-in-Publication Data
AMS Special Session in Memory of Daryl Geller on Wavelet and Frame Theoretic Methods in
HarmonicAnalysisandPartialDifferentialEquations(2012: Rochester,N.Y.)
Commutativeandnoncommutativeharmonicanalysisandapplications: AMSSpecialSession
in Memory of Daryl Geller on Wavelet and Frame Theoretic Methods in Harmonic Analysis
and Partial Differential Equations, September 22–23, 2012, Rochester Institute of Technology,
Rochester,NY/AzitaMayeli,AlexIosevich,PalleE.T.Jorgensen,GesturO´lafsson,editors.
pagescm. –(Contemporarymathematics;volume603)
Includesbibliographicalreferences.
ISBN978-0-8218-9493-4(alk. paper)
1. Harmonic analysis–Congresses. 2. Differential equations, Partial–Congresses. I. Mayeli,
Azita,1976-editorofcompilation. II.Title.
QA403.A5275 2012
515(cid:2).53–dc23 2013018563
ContemporaryMathematicsISSN:0271-4132(print);ISSN:1098-3627(online)
DOI:http://dx.doi.org/10.1090/conm/603
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To the memory of Daryl Geller;
man of the Heisenberg group.

Contents
Preface ix
Remembering Daryl Geller xi
Publications xiii
List of speakers xvii
List of participants xix
Part I: Noncommutative Harmonic Analysis
Krein-space operators induced by Dirichlet characters
Ilwoo Cho and Palle E. T. Jorgensen 3
Noncommutative solenoids and their projective modules
Fr´ed´eric Latr´emoli`ere and Judith A. Packer 35
Paley-Wiener-Schwartz nearly Parseval frames on noncompact symmetric
spaces
Isaac Z. Pesenson 55
Projective multiresolution analyses over irrational rotation algebras
Benjamin Purkis 73
Part II: Commutative Harmonic Analysis
Regularity of abelian linear actions
Didier Arnal, B´echir Dali, Bradley Currey,
and Vignon Oussa 89
n-widths and approximation theory on compact Riemannian manifolds
Daryl Geller and Isaac Z. Pesenson 111
A four dimensional continuous wavelet transform
Mahya Ghandehari, Aizhan Syzdykova, and Keith F. Taylor 123
Part III: Applications
Dynamical sampling in shift-invariant spaces
Roza Aceska, Akram Aldroubi, Jacqueline Davis,
and Armenak Petrosyan 139
vii
viii CONTENTS
High-frequency tail index estimation by nearly tight frames
Claudio Durastanti and Xiaohong Lan 149
Multiplexing and demultiplexing frame pairs
Azita Mayeli and Mohammad Razani 189
Preface
In recent years, wavelet and frame theory advances in harmonic analysis have
spawned new and exciting developments in various areas and have revealed some
novel and unexpected connections between different parts of mathematics, pure
andapplied. Forexample,theuseofwaveletandframetheorymethods,multiscale
analysis methods, and Calder´on decomposition techniques have played a crucial
role in a diverse range of problems in pure and applied mathematics and statistics.
Thisvolumeconsistsofinvitedsurveyandexpositionsstressingtheinteraction
and connectionbetweenDarly Geller’s areaof research: commutative and abstract
harmonic analysis, in particular harmonic analysis on the Heisenberg group. The
invitedpotentialauthorsofthisvolumehavealreadymadesubstantialcontributions
to mathematics and its applications.
Thecontentofthevolumeisbasedonunderlyingfundamentalideasofrelevance
to the formal presentations at the conference for future research. Each article
contains new research advances, and starts with a user friendly tutorial to make
this volume accessible to young mathematicians.
For the purpose of organization, we have divided the book into three parts,
noncommutative, commutative, and applications: The first group of papers is de-
voted to problems in noncommutative harmonic analysis, the second to topics in
commutative harmonic analysis, and the papers in the third grouping are devoted
to such applications as wavelet and frame theory, and to some real-world applica-
tions. Although some papers in the book in fact cover more than one of the three
areas, we feel that a subdivision into three separate parts will still prove useful to
readers.
The Editors:
Azita Mayeli
Alex Iosevich
Palle Jorgensen
Gestur O´lafsson
April 23, 2013
ix