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Introduction to the Theory of Banach Representations of Groups

  • Book
  • © 1988

Overview

Authors:
  1. Yurii I. Lyubich

    1. Khar’kovskii Universitet, Khar’kov, Russia

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Part of the book series: Operator Theory: Advances and Applications (OT, volume 30)

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Table of contents (5 chapters)

  1. Front Matter

    Pages I-IX
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  2. Elements of Spectral Theory

    • Yurii I. Lyubich
    Pages 1-44

  3. Topological Groups and Semigroups

    • Yurii I. Lyubich
    Pages 45-76

  4. Elements of General Representation Theory

    • Yurii I. Lyubich
    Pages 77-121

  5. Representations of Compact Semigroups

    • Yurii I. Lyubich
    Pages 123-185

  6. Representations of Locally Compact Abelian Groups

    • Yurii I. Lyubich
    Pages 187-208

  7. Back Matter

    Pages 209-225
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Keywords

About this book

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.

Authors and Affiliations

  • Khar’kovskii Universitet, Khar’kov, Russia

    Yurii I. Lyubich

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