Principles of Harmonic Analysis/ by Anton Deitmar, Siegfried Echterhoff.

By: Deitmar, AntonContributor(s): Echterhoff, Siegfried, 1960-Material type: TextTextPublication details: Cham : Springer International Publishing : Imprint: Springer, 2014Edition: 2nd edDescription: XIII, 332 pISBN: 9783319709482 (pbk)Subject(s): Mathematics | Harmonic analysis | VisualizationGenre/Form: Electronic books.DDC classification: 515.785 Online resources: Full text available from Springer Mathematics and Statistics eBooks 2014 English/International
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.
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.
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Holdings
Item type Current library Call number Copy number Status Date due Barcode Item holds
Books Books Namal Library
Mathematics 		515.785 DEI-P 2018 10905 (Browse shelf (Opens below)) 1 Available 0010905
Books Books Namal Library
Mathematics 		515.785 DEI-P 2018 10904 (Browse shelf (Opens below)) 2 Available 0010904
Total holds: 0

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.

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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