Bibliograph

Principles of Harmonic Analysis, by Anton Deitmar, Siegfried Echterhoff

Type

Label

Principles of Harmonic Analysis, by Anton Deitmar, Siegfried Echterhoff

Language

eng

resource.imageBitDepth

Literary Form

non fiction

Main title

Principles of Harmonic Analysis

Medium

electronic resource

Oclc number

892539570

Responsibility statement

by Anton Deitmar, Siegfried Echterhoff

Series statement

Universitext,, 0172-5939Springer eBooks

Summary

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

Table Of Contents

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

Contributor

Creator