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Introduction to the Theory of Banach Representations of Groups : Operator Theory: Advances and Applications - Yurii I. Lyubich

Introduction to the Theory of Banach Representations of Groups

Operator Theory: Advances and Applications

Paperback Published: 1988
ISBN: 9783764322076
Number Of Pages: 224

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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.

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.

ISBN: 9783764322076
ISBN-10: 3764322071
Series: Operator Theory: Advances and Applications
Audience: General
Format: Paperback
Language: English
Number Of Pages: 224
Published: 1988
Publisher: Birkhauser Verlag AG
Country of Publication: CH
Dimensions (cm): 24.41 x 16.99  x 1.3
Weight (kg): 0.39