Principles of Harmonic Analysis
Seiten
2014
|
2nd ed. 2014
Springer International Publishing (Verlag)
978-3-319-05791-0 (ISBN)
Springer International Publishing (Verlag)
978-3-319-05791-0 (ISBN)
This book examines 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.
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.
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.
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.
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.
| Erscheint lt. Verlag | 11.7.2014 |
|---|---|
| Reihe/Serie | Universitext |
| Zusatzinfo | XIII, 332 p. 11 illus. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 655 g |
| Themenwelt | Informatik ► Software Entwicklung ► User Interfaces (HCI) |
| Mathematik / Informatik ► Mathematik ► Analysis | |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Mathematik / Informatik ► Mathematik ► Graphentheorie | |
| Schlagworte | Abelian Groups • Analysis • Direct and Indirect Integrals • fourier analysis • Harmonic Analysis • Pontryagin Duality • Selberg trace formula |
| ISBN-10 | 3-319-05791-X / 331905791X |
| ISBN-13 | 978-3-319-05791-0 / 9783319057910 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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