Introduction to the Theory of Banach Representations of Groups: 30 - Brossura

Lyubich, Yurii I.

Brossura

ISBN 10: 3764322071 ISBN 13: 9783764322076

Casa editrice: Springer, 2013

Riassunto

The theory of group representations plays an important roie in modern mathematics and its applica~ions to natural sciences. In the compulsory university curriculum it is included as a branch of algebra, dealing with representations of finite groups (see, for example, the textbook of A. I. Kostrikin [25]). The representation theory for compact, locally compact Abelian, and Lie groups is co­ vered in graduate courses, concentrated around functional analysis. The author of the present boo~ has lectured for many years on functional analysis at Khar'kov University. He subsequently con­ tinued these lectures in the form of a graduate course on the theory of group representations, in which special attention was devoted to a retrospective exposition of operator theory and harmo­ nic analysis of functions from the standpoint of representation theory. In this approach it was natural to consider not only uni­ tary, but also Banach representations, and not only representations of groups, but also of semigroups.

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Contenuti

1 — Elements of Spectral Theory.- 1. Integration of vector-valued functions.- 2. Linear operators in Banach space.- 3. Spectrum and resolvent of linear operators.- 4. Invariant subspaces.- 5. Commutative Banach algebras.- 2 — Topological Groups and Semigroups.- 1. Topological groups.- 2. Topological semigroups.- 3. Invariant measures and means.- 3 — Elements of General Representation Theory.- 1. Actions and representations.- 2. Decomposition of representations.- 3. Finite dimensional representations.- 4. The representation spectrum of an Abelian semigroup.- 4 — Representations of Compact Semigroups.- 1. Harmonic analysis on compact groups.- 2. Banach representations of compact groups and semigroups.- 3. Almost periodic representations and functions.- 4. Nonnegative a.p. representations.- 5 — Representations of Locally Compact Abelian Groups.- 1. Elements of harmonic analysis.- 2. Representations with separable spectrum.- References.- Books.- Journal Articles.

Dettagli dell'edizione

• Editore: Springer
• Data di pubblicazione: 2013
• Lingua: Inglese
• ISBN 10: 3764322071
• ISBN 13: 9783764322076
• Rilegatura: Copertina flessibile
• Numero di pagine: 240
• Contatto del produttore: non disponibile
• Persona responsabile: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Germania