Principles of harmonic analysis /
Deitmar, Anton.
Principles of harmonic analysis / Anton Deitmar, Siegfried Echterhoff. - 2nd ed. - New York : Springer, c2009. - xv, 333 p. ; 24 cm. - Universitext .
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.
9783319709482 9780387854687 (pbk.) 038785469X (ebk.) 9780387854694 (ebk.)
2008938333
GBA903240 bnb
014858379 Uk
Harmonic analysis.
QA403 / .D45 2009
515.243 / DEI
Principles of harmonic analysis / Anton Deitmar, Siegfried Echterhoff. - 2nd ed. - New York : Springer, c2009. - xv, 333 p. ; 24 cm. - Universitext .
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.
9783319709482 9780387854687 (pbk.) 038785469X (ebk.) 9780387854694 (ebk.)
2008938333
GBA903240 bnb
014858379 Uk
Harmonic analysis.
QA403 / .D45 2009
515.243 / DEI