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Principles of Harmonic Analysis de Anton Deitmar

Principles of Harmonic Analysis

Autor Anton Deitmar, Siegfried Echterhoff
en Limba Engleză Paperback – 17 sep 2016
This book offers a complete and streamlined treatment of the central principles of abelian harmonic analysis: Pontryagin duality, the Plancherel theorem and the Poisson summation formula, as well as their respective generalizations to non-abelian groups, including the Selberg trace formula. The principles are then applied to spectral analysis of Heisenberg manifolds and Riemann surfaces. This new edition contains a new chapter on p-adic and adelic groups, as well as a complementary section on direct and projective limits. Many of the supporting proofs have been revised and refined. The book is an excellent resource for graduate students who wish to learn and understand harmonic analysis and for researchers seeking to apply it.
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Specificații

ISBN-13: 9783319379043
ISBN-10: 3319379046
Pagini: 348
Ilustrații: XIII, 332 p. 11 illus.
Dimensiuni: 155 x 235 x 19 mm
Greutate: 0.53 kg
Ediția:Softcover reprint of the original 2nd edition 2014
Editura: Springer
Locul publicării:Cham, Switzerland

Cuprins

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.

Notă biografică

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.

Textul de pe ultima copertă

This book offers a complete and streamlined treatment of the central principles of abelian harmonic analysis: Pontryagin duality, the Plancherel theorem and the Poisson summation formula, as well as their respective generalizations to non-abelian groups, including the Selberg trace formula. The principles are then applied to spectral analysis of Heisenberg manifolds and Riemann surfaces. This new edition contains a new chapter on p-adic and adelic groups, as well as a complementary section on direct and projective limits. Many of the supporting proofs have been revised and refined. The book is an excellent resource for graduate students who wish to learn and understand harmonic analysis and for researchers seeking to apply it.

Caracteristici

Second edition is completely revised and updated, including many new exercises and theorems New chapter on p-adic and abelic groups Updated appendices on theoretic topology, Lebesgue integration, and functional analysis Includes supplementary material: sn.pub/extras

Recenzii

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)