Verfügbarkeit: Principles of harmonic analysis | Technische Universität München

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Bibliographische Detailangaben
Beteiligte Personen:	Deitmar, Anton 1960- (VerfasserIn), Echterhoff, Siegfried 1960- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	New York, NY Springer 2009
Schriftenreihe:	Universitext
Schlagwörter:	Harmonic analysis Harmonische Analyse
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017056016&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XV, 333 S.
ISBN:	9780387854687 9780387854694

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Datensatz im Suchindex

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DE-BY-UBR_location	UB Lesesaal Mathematik UB Lesesaal Mathematik UB Lesesaal Mathematik UB Handapparat Mathematik Prof. Künnemann
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adam_text	Contents 1 Haar Integration 1 1.1 Topological Groups .................... 1 1.2 Locally Compact Groups ................. 6 1.3 Haar Measure ....................... 8 1.4 The Modular Function .................. 17 1.5 The Quotient Integral Formula ............. 21 1.6 Convolution ........................ 25 1.7 The Fourier Transform .................. 29 1.8 Exercises ......................... 30 2 Banach Algebras 33 2.1 Banach Algebras ..................... 33 2.2 The Spectrum σΑ(α) ................... 37 2.3 Adjoining a Unit ..................... 41 2.4 The Gelfand Map ..................... 43 2.5 Maximal Ideals ...................... 47 2.6 The Gelfand-Naimark Theorem ............. 49 2.7 The Continuous Functional Calculus .......... 54 2.8 Exercises and Notes ................... 58 3 Duality for Abelian Groups 63 xi xii CONTENTS 3.1 The Dual Group ..................... 63 3.2 The Fourier Transform .................. 67 3.3 The C-Algebra of an LCA-Group ........... 69 3.4 The Plancherel Theorem ................. 72 3.5 Pontryagin Duality .................... 78 3.6 The Poisson Summation Formula ............ 83 3.7 Exercises and Notes ................... 86 4 The Structure of LCA-Groups 91 4.1 Connectedness ...................... 91 4.2 The Structure Theorems ................. 95 4.3 Exercises .........................107 5 Operators on Hubert Spaces 109 5.1 Functional Calculus ...................109 5.2 Compact Operators ...................115 5.3 Hilbert-Schmidt and Trace Class ............119 5.4 Exercises .........................124 6 Representations 127 6.1 Schur s Lemma ......................127 6.2 Representations of L1 (G) ................131 6.3 Exercises .........................135 7 Compact Groups 139 7.1 Finite Dimensional Representations ...........139 7.2 The Peter-Weyl Theorem ................141 7.3 Isotypes ..........................145 7.4 Induced Representations .................148 CONTENTS xiii 7.5 Representations of SU(2) ................150 7.6 Exercises .........................156 8 Direct Integrals 159 8.1 Von Neumann Algebras .................159 8.2 Weak and Strong Topologies ..............160 8.3 Representations ......................162 8.4 Hubert Integrals .....................165 8.5 The Plancherel Theorem .................167 8.6 Exercises .........................169 9 The Selberg Trace Formula 171 9.1 Cocompact Groups and Lattices ............171 9.2 Discreteness of the Spectrum ..............174 9.3 The Trace Formula ....................179 9.4 Locally Constant Functions ...............185 9.5 Exercises and Notes ...................186 10 The Heisenberg Group 189 10.1 Definition .........................189 10.2 The Unitary Dual ....................190 10.3 The Plancherel Theorem for Я .............195 10.4 The Standard Lattice ..................196 10.5 Exercises and Notes ...................199 11 SL2(K) 201 11.1 The Upper Half Plane ..................201 11.2 The Hecke Algebra ....................205 11.3 An Explicit Plancherel Theorem ............214 xiv CONTENTS 11.4 The Trace Formula ....................216 11.5 Weyl s Asymptotic Law .................222 11.6 The Selberg Zeta Function ................225 11.7 Exercises and Notes ...................229 12 Wavelets 233 12.1 First Ideas .........................233 12.2 Discrete Series Representations .............239 12.3 Examples of Wavelet Transforms ............246 12.4 Exercises and Notes ...................255 A Topology 259 A.I Generators and Countability ..............260 A.2 Continuity .........................261 A.3 Compact Spaces .....................262 A.4 Hausdorff Spaces .....................264 A. 5 Initial- and Final-Topologies ...............265 A.6 Nets ............................267 A.7 Tychonov s Theorem ...................271 A.8 The Lemma of Urysohn .................273 A.9 Baire Spaces .......................275 A.1Ü The Stone- Weierstraß Theorem .............276 В Measure and Integration 281 B.I Measurable Functions and Integration .........281 B.2 The Riesz Representation Theorem ...........285 B.3 Fubinľs Theorem .....................287 B.4 Lp-Sphces and the Riesz-Fischer Theorem ..........................291 CONTENTS xv В. 5 The Radon-Nikodym Theorem .............296 B.6 Vector-Valued Integrals .................297 С Functional Analysis 305 C.I Basic Concepts ......................305 C.2 Seminorms ........................311 C.3 Hilbert Spaces ......................313 C.4 Unbounded Operators ..................316 Bibiliography 323 Index 329
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dewey-search	515.2433
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isbn	9780387854687 9780387854694
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-017056016
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spellingShingle	Deitmar, Anton 1960- Echterhoff, Siegfried 1960- Principles of harmonic analysis Harmonic analysis Harmonische Analyse (DE-588)4023453-8 gnd
subject_GND	(DE-588)4023453-8
title	Principles of harmonic analysis
title_auth	Principles of harmonic analysis
title_exact_search	Principles of harmonic analysis
title_full	Principles of harmonic analysis Anton Deitmar ; Siegfried Echterhoff
title_fullStr	Principles of harmonic analysis Anton Deitmar ; Siegfried Echterhoff
title_full_unstemmed	Principles of harmonic analysis Anton Deitmar ; Siegfried Echterhoff
title_short	Principles of harmonic analysis
title_sort	principles of harmonic analysis
topic	Harmonic analysis Harmonische Analyse (DE-588)4023453-8 gnd
topic_facet	Harmonic analysis Harmonische Analyse
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017056016&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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