Stochastic Models, Information Theory, and Lie Groups Volume 2.pdf

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Stochastic Models, Information Theory, and Lie Groups, Volume 2

ANHA Series Preface

Preface

Contents

10 Lie Groups I: Introduction and Examples

11 Lie Groups II: Differential-Geometric Properties

12 Lie Groups III: Integration, Convolution,and Fourier Analysis

13 Variational Calculus on Lie Groups

14 Statistical Mechanics and Ergodic Theory

15 Parts Entropy and the Principal Kinematic Formula

16 Multivariate Statistical Analysis and Random Matrix Theory

17 Information, Communication, and Group Theory

18 Algebraic and Geometric Coding Theory

19 Information Theory on Lie Groups

20 Stochastic Processes on Lie Groups

21 Locomotion and Perception as Communication over Principal Fiber Bundles

22 Summary

Index

Gitta Kutyniok Technische Universität Berlin Berlin, Germany Zuowei Shen National University of Singapore Singapore AppliedandNumericalHarmonicAnalysisSeriesEditorJohnJ.BenedettoUniversityofMarylandCollegePark,MD,USAEditorialAdvisoryBoardAkramAldroubiVanderbiltUniversityNashville,TN,USAAndreaBertozziUniversityofCaliforniaLosAngeles,CA,USADouglasCochranArizonaStateUniversityPhoenix,AZ,USAHansG.FeichtingerUniversityofViennaVienna,AustriaChristopherHeilGeorgiaInstituteofTechnologyAtlanta,GA,USAStéphaneJaffardUniversityofParisXIIParis,FranceJelenaKovaˇcevi´cCarnegieMellonUniversityPittsburgh,PA,USAMauroMaggioniDukeUniversityDurham,NC,USAThomasStrohmerUniversityofCaliforniaDavis,CA,USAYangWangMichiganStateUniversityEastLansing,MI,USA

Stochastic Models, Information Theory, and Lie Groups, Volume 2 Analytic Methods and Modern Applications Gregory S. Chirikjian

ISBN 978-0-8176- -2 DOI 10.1007/978-0-8176- Springer New York Dordrecht Heidelberg London 4944-9 4943 e-ISBN 978-0-8176- 4944-9 Library of Congress Control Number: 2011941792 Mathematics Subject Classification 94A15, 94A17 (2010): 2E60, 53Bxx, 53C65, 58A15, 58J65, 60D05, 60H10, 70G45, 82C31, 2 © Springer Science+Business Media, LLC 2012 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Birkhäuser Boston, c/o Springer Science+Business Media, LLC, 233 Springer Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Sc ience+Business Media (www.birkhauser-science.com) Gregory S. ChirikjianDepartment of Mechanical EngineeringThe Johns Hopkins UniversityBaltimore, MD 21218-2682USAgregc@jhu.edu

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ANHASeriesPrefaceTheAppliedandNumericalHarmonicAnalysis(ANHA)bookseriesaimstoprovidetheengineering,mathematical,andscientiﬁccommunitieswithsigniﬁcantdevelopmentsinharmonicanalysis,rangingfromabstractharmonicanalysistobasicapplications.Thetitleoftheseriesreﬂectstheimportanceofapplicationsandnumericalimplementation,butrichnessandrelevanceofapplicationsandimplementationdependfundamentallyonthestructureanddepthoftheoreticalunderpinnings.Thus,fromourpointofview,theinterleavingoftheoryandapplicationsandtheircreativesymbioticevolutionisaxiomatic.Harmonicanalysisisawellspringofideasandapplicabilitythathasﬂourished,de-veloped,anddeepenedovertimewithinmanydisciplinesandbymeansofcreativecross-fertilizationwithdiverseareas.Theintricateandfundamentalrelationshipbe-tweenharmonicanalysisandﬁeldssuchassignalprocessing,partialdiﬀerentialequa-tions(PDEs),andimageprocessingisreﬂectedinourstate-of-the-artANHAseries.Ourvisionofmodernharmonicanalysisincludesmathematicalareassuchaswavelettheory,Banachalgebras,classicalFourieranalysis,time-frequencyanalysis,andfractalgeometry,aswellasthediversetopicsthatimpingeonthem.Forexample,wavelettheorycanbeconsideredanappropriatetooltodealwithsomebasicproblemsindigitalsignalprocessing,speechandimageprocessing,geophysics,patternrecognition,biomedicalengineering,andturbulence.Theseareasimplementthelatesttechnologyfromsamplingmethodsonsurfacestofastalgorithmsandcom-putervisionmethods.TheunderlyingmathematicsofwavelettheorydependsnotonlyonclassicalFourieranalysis,butalsoonideasfromabstractharmonicanalysis,includ-ingvonNeumannalgebrasandtheaﬃnegroup.ThisleadstoastudyoftheHeisenberggroupanditsrelationshiptoGaborsystems,andofthemetaplecticgroupforamean-ingfulinteractionofsignaldecompositionmethods.Theunifyinginﬂuenceofwavelettheoryintheaforementionedtopicsillustratesthejustiﬁcationforprovidingameansforcentralizinganddisseminatinginformationfromthebroader,butstillfocused,areaofharmonicanalysis.ThiswillbeakeyroleofANHA.Weintendtopublishwiththescopeandinteractionthatsuchahostofissuesdemands.Alongwithourcommitmenttopublishmathematicallysigniﬁcantworksatthefrontiersofharmonicanalysis,wehaveacomparablystrongcommitmenttopublishmajoradvancesinthefollowingapplicabletopicsinwhichharmonicanalysisplaysasubstantialrole:vii

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