Principles of Harmonic Analysis

Anton Deitmar, Siegfried Echterhoff

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English

Springer International Publishing AG
17 September 2016

Complex analysis, complex variables; Functional analysis & transforms; Combinatorics & graph theory; Applied mathematics

Series: Universitext

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.

By: Anton Deitmar, Siegfried Echterhoff
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: Softcover reprint of the original 2nd ed. 2014
Dimensions: Height: 235mm, Width: 155mm, Spine: 18mm
Weight: 534g
ISBN: 9783319379043
ISBN 10: 3319379046
Series: Universitext
Pages: 332
Publication Date: 17 September 2016
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

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.

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.