Anton Deitmar, Siegfried Echterhoff

Principles of Harmonic Analysis (eBook, PDF)

• Format: PDF

Produktbeschreibung

The present book is intended as a text for a graduate course on abstract harmonic analysis and its applications. The book can be used as a follow up to Anton Deitmer's previous book, A First Course in Harmonic Analysis, or independently, if the students already have a modest knowledge of Fourier Analysis. In this book, among other things, proofs are given of Pontryagin Duality and the Plancherel Theorem for LCA-groups, which were mentioned but not proved in A First Course in Harmonic Analysis. Using Pontryagin duality, the authors also obtain various structure theorems for locally compact abelian groups. The book then proceeds with Harmonic Analysis on non-abelian groups and its applications to theory in number theory and the theory of wavelets.

Knowledge of set theoretic topology, Lebesgue integration, and functional analysis on an introductory level will be required in the body of the book. For the convenience of the reader, all necessary ingredients from these areas have been included in the appendices.

Professor Deitmar is Professor of Mathematics at the University of Tübingen, Germany. He is a former Heisenberg fellow and has taught in the U.K. for some years. Professor Echterhoff is Professor of Mathematics and Computer Science at the University of Münster, Germany.

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Produktdetails

• Verlag: Springer-Verlag GmbH
• Seitenzahl: 333
• Erscheinungstermin: 4. Dezember 2008
• Englisch
• ISBN-13: 9780387854694
• Artikelnr.: 43732048

Autorenporträt

Anton Deitmar is a professor of Mathematics at the University of Tübingen, Germany. Siegfried Echterhoff is a professor of Mathematics at the University of Münster, Germany.

Inhaltsangabe

1. Haar Integration.- 2. Banach Algebras.- 3. Duality for Abelian Groups.- 4. The Structure of LCA-Groups.- 5. Operators on Hilbert Spaces.- 6. Representations.- 7. Compact Groups.- 8. Direct Integrals.- 9. The Selberg Trace Formula.- 10. The Heisenberg Group.- 11. SL2(R).- 12. Wavelets.- 13. p-adic numbers and adeles.- A. Topology.- B. Measure and Integration.- C: Functional Analysis.

Rezensionen

From the reviews:

"Principles of Harmonic Analysis is an excellent and thorough introduction to both commutative and non-commutative harmonic analysis. It is suitable for any graduates student with the appropriate background ... . In summary, this is a superb book. ... it is extremely readable and well organized. Graduate students, and other newcomers to the field, will greatly appreciate the author's clear and careful writing." (Kenneth A. Ross, MAA Online, February, 2009)

"The book under review is a nice presentation of all the standard, basic material on abstract harmonic analysis. ... The most welcome aspect of the book under review is the inclusion of a discussion of the trace formula, a rather unusual feature in an introductory book on harmonic analysis. ... This is a nice addition to the literature on the subject." (Krishnan Parthasarathy, Mathematical Reviews, Issue 2010 g)