Siegfried Echterhoff's Books

Principles of Harmonic Analysis

By: Anton Deitmar,Siegfried Echterhoff

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Principles of Harmonic Analysis

By: Anton Deitmar,Siegfried Echterhoff

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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Page Count

330

Publisher

Springer

Published Date

ISBN 10

3319057928

ISBN 13

9783319057927

A Categorical Approach to Imprimitivity Theorems for $C^*$-Dynamical Systems

By: Siegfried Echterhoff

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A Categorical Approach to Imprimitivity Theorems for $C^*$-Dynamical Systems

By: Siegfried Echterhoff

It has become apparent that studying the representation theory and structure of crossed-product C*-algebras requires imprimitivity theorems. This monograph shows that the imprimitivity theorem for reduced algebras, Green's imprimitivity theorem for actions of groups, and Mansfield's imprimitivity theorem for coactions of groups can all be understoo

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Page Count

186

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821838571

ISBN 13

9780821838570

K-Theory for Group C-Algebras and Semigroup C-Algebras

By: Joachim Cuntz,Siegfried Echterhoff,Xin Li,Guoliang Yu

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K-Theory for Group C-Algebras and Semigroup C-Algebras

By: Joachim Cuntz,Siegfried Echterhoff,Xin Li,Guoliang Yu

This book gives an account of the necessary background for group algebras and crossed products for actions of a group or a semigroup on a space and reports on some very recently developed techniques with applications to particular examples. Much of the material is available here for the first time in book form. The topics discussed are among the most classical and intensely studied C*-algebras. They are important for applications in fields as diverse as the theory of unitary group representations, index theory, the topology of manifolds or ergodic theory of group actions. Part of the most basic structural information for such a C*-algebra is contained in its K-theory. The determination of the K-groups of C*-algebras constructed from group or semigroup actions is a particularly challenging problem. Paul Baum and Alain Connes proposed a formula for the K-theory of the reduced crossed product for a group action that would permit, in principle, its computation. By work of many hands, the formula has by now been verified for very large classes of groups and this work has led to the development of a host of new techniques. An important ingredient is Kasparov's bivariant K-theory. More recently, also the C*-algebras generated by the regular representation of a semigroup as well as the crossed products for actions of semigroups by endomorphisms have been studied in more detail. Intriguing examples of actions of such semigroups come from ergodic theory as well as from algebraic number theory. The computation of the K-theory of the corresponding crossed products needs new techniques. In cases of interest the K-theory of the algebras reflects ergodic theoretic or number theoretic properties of the action.

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Page Count

325

Publisher

Birkhäuser

Published Date

ISBN 10

3319599151

ISBN 13

9783319599151

Crossed Products with Continuous Trace

By: Siegfried Echterhoff

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Crossed Products with Continuous Trace

By: Siegfried Echterhoff

This memoir presents an extensive study of strongly continuous actions of abelian locally compact groups on [italic capital]C*-algebras with continuous trace. Expositions of the Mackey-Green-Rieffel machine of induced representations and the theory of Morita equivalent [italic capital]C*-dynamical systems are included. There is also an elaboration of the representation theory of crossed products by actions of abelian groups on type I [italic capital]C*-algebras.

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Page Count

149

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821805630

ISBN 13

9780821805633

Principles of Harmonic Analysis

By: Anton Deitmar,Siegfried Echterhoff

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Principles of Harmonic Analysis

By: Anton Deitmar,Siegfried Echterhoff

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Page Count

330

Publisher

Springer

Published Date

ISBN 10

3319057928

ISBN 13

9783319057927

K-Theory for Group C-Algebras and Semigroup C-Algebras

By: Joachim Cuntz,Siegfried Echterhoff,Xin Li,Guoliang Yu

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K-Theory for Group C-Algebras and Semigroup C-Algebras

By: Joachim Cuntz,Siegfried Echterhoff,Xin Li,Guoliang Yu

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N/A

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Solve jigsaw puzzle

Age

Page Count

325

Publisher

Birkhäuser

Published Date

ISBN 10

3319599151

ISBN 13

9783319599151

Book's by Siegfried Echterhoff

Principles of Harmonic Analysis

Principles of Harmonic Analysis

A Categorical Approach to Imprimitivity Theorems for $C^*$-Dynamical Systems

A Categorical Approach to Imprimitivity Theorems for $C^*$-Dynamical Systems

K-Theory for Group C-Algebras and Semigroup C-Algebras

K-Theory for Group C-Algebras and Semigroup C-Algebras

Crossed Products with Continuous Trace

Crossed Products with Continuous Trace

Principles of Harmonic Analysis

Principles of Harmonic Analysis

K-Theory for Group C-Algebras and Semigroup C-Algebras

K-Theory for Group C-Algebras and Semigroup C-Algebras

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