Introduction to Harmonic Analysis and Generalized Gelfand Pairs (eBook)

Gerrit van Dijk (Autor)

eBook Download: PDF

2009
232 Seiten
De Gruyter (Verlag)
978-3-11-022020-9 (ISBN)

Infos

Harmonic analysis is the branch of mathematics that studies the representation of functions or signals as the superposition of basic waves, and Gelfand pairs refer to pairs of groups satisfying certain properties on restricted representations. This book contains written material of lectures on the topic which might serve as an introduction to the topic.

Gerrit van Dijk, Leiden University, Netherlands

Autor

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Gerrit van Dijk, Leiden University, Netherlands

Inhalt

Preface 5
Contents 7
1 Fourier Series 11
2 Fourier Integrals 17
3 Locally Compact Groups 35
4 Haar Measures 42
5 Harmonic Analysis on Locally Compact Abelian Groups 59
6 Classical Theory of Gelfand Pairs 85
7 Examples of Gelfand Pairs 99
8 Theory of Generalized Gelfand Pairs 141
9 Examples of Generalized Gelfand Pairs 162
Appendix A The Averaging Mapping on the Space RnC1 205
Appendix B The Averaging Mapping on the Space X 220
Bibliography 227
Index 231

Rezensionen

lt;P>"The book under review is basically self-contained, only requiring basic functional analysis, some knowledge of distribution theory and elementary Lie theory. The material presented in the book is carefully explained so that it can be used for self-study." Mathematical Reviews

Produkt-Details

• Erscheint lt. Verlag: 23.12.2009
• Reihe/Serie: De Gruyter Studies in Mathematics
• Reihe/Serie: De Gruyter Studies in Mathematics
• Reihe/Serie: ISSN
• Reihe/Serie: ISSN
• Verlagsort: Berlin/Boston
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Technik
• Schlagworte: Analysis • Gelfand • Generalized Gelfand Pairs • Harmonic Analysis • locally compact abelian groups • Lokalkompakte Gruppe
• ISBN-10: 3-11-022020-2 / 3110220202
• ISBN-13: 978-3-11-022020-9 / 9783110220209