Anton Deitmar, Siegfried Echterhoff

Principles of Harmonic Analysis

• Broschiertes Buch

Produktbeschreibung

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.

Produktdetails

• Universitext
• Verlag: Springer / Springer International Publishing / Springer, Berlin
• Artikelnr. des Verlages: 978-3-319-37904-3
• 2. Aufl.
• Seitenzahl: 348
• Erscheinungstermin: 17. September 2016
• Englisch
• Abmessung: 235mm x 155mm x 19mm
• Gewicht: 528g
• ISBN-13: 9783319379043
• ISBN-10: 3319379046
• Artikelnr.: 45753224

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)