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Principles of harmonic analysis / Anton Deitmar, Siegfried Echterhoff.

By: Contributor(s): Material type: TextSeries: UniversitextPublication details: New York : Springer, c2009.Edition: 2nd edDescription: xv, 333 p. ; 24 cmISBN:
  • 9783319709482
  • 9780387854687 (pbk.)
  • 038785469X (ebk.)
  • 9780387854694 (ebk.)
Subject(s): DDC classification:
  • 515.243 22 DEI
LOC classification:
  • QA403 .D45 2009
Contents:
Haar Integration Anton Deitmar, Siegfried Echterhoff Pages 1-35 Banach Algebras Anton Deitmar, Siegfried Echterhoff Pages 37-60 Duality for Abelian Groups Anton Deitmar, Siegfried Echterhoff Pages 61-83 The Structure of LCA-Groups Anton Deitmar, Siegfried Echterhoff Pages 85-106 Operators on Hilbert Spaces Anton Deitmar, Siegfried Echterhoff Pages 107-121 Representations Anton Deitmar, Siegfried Echterhoff Pages 123-131 Compact Groups Anton Deitmar, Siegfried Echterhoff Pages 133-151 Direct Integrals Anton Deitmar, Siegfried Echterhoff Pages 153-163 The Selberg Trace Formula Anton Deitmar, Siegfried Echterhoff Pages 165-183 The Heisenberg Group Anton Deitmar, Siegfried Echterhoff Pages 185-194 Anton Deitmar, Siegfried Echterhoff Pages 195-223 Wavelets Anton Deitmar, Siegfried Echterhoff Pages 225-245 p-Adic Numbers and Adeles Anton Deitmar, Siegfried Echterhoff Pages 247-267 Back Matter Pages 269-332
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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Project book CUTN Central Library Sciences Non-fiction 515.243 DEI (Browse shelf(Opens below)) Checked out to Renuka Devi V (20019T) 31/01/2024 48891

Includes bibliographical references (p.323-327) and index.

Haar Integration
Anton Deitmar, Siegfried Echterhoff
Pages 1-35
Banach Algebras
Anton Deitmar, Siegfried Echterhoff
Pages 37-60
Duality for Abelian Groups
Anton Deitmar, Siegfried Echterhoff
Pages 61-83
The Structure of LCA-Groups
Anton Deitmar, Siegfried Echterhoff
Pages 85-106
Operators on Hilbert Spaces
Anton Deitmar, Siegfried Echterhoff
Pages 107-121
Representations
Anton Deitmar, Siegfried Echterhoff
Pages 123-131
Compact Groups
Anton Deitmar, Siegfried Echterhoff
Pages 133-151
Direct Integrals
Anton Deitmar, Siegfried Echterhoff
Pages 153-163
The Selberg Trace Formula
Anton Deitmar, Siegfried Echterhoff
Pages 165-183
The Heisenberg Group
Anton Deitmar, Siegfried Echterhoff
Pages 185-194
Anton Deitmar, Siegfried Echterhoff
Pages 195-223
Wavelets
Anton Deitmar, Siegfried Echterhoff
Pages 225-245
p-Adic Numbers and Adeles
Anton Deitmar, Siegfried Echterhoff Pages 247-267
Back Matter Pages 269-332

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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