Harmonic Analysis in Hypercomplex Systems by Yu.M. BerezanskyHarmonic Analysis in Hypercomplex Systems by Yu.M. Berezansky

Harmonic Analysis in Hypercomplex Systems

byYu.M. Berezansky

Paperback | December 7, 2010

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This monograph is devoted to the theory of hypercomplex systems with locally compact basis. Such systems were introduced by Yu. Berezansky and S. Krein in the 1950s and are a generalisation of the notion of a hypergroup (a family of generalised shift operators) which was introduced in the 1970s. The book gives a state-of-the-art account of hypercomplex systems theory. After the introductory chapter, it treats the Lie theory of hypercomplex systems and examples. Topics covered include Fourier transforms, the Plancherel theorem, the Peter-Weyl theorem, representation theory, duality, Gelfand pairs, Sturm-Liouville operators, and Lie theory. New proofs of results concerning Tannaka-Krein duality and Gelfand pairs are given. On the basis of this theory, new approaches to the construction of harmonic analysis on well-known objects become possible. Audience: This volume will be of interest to researchers and graduate students involved in harmonic analysis and representation theory.
Title:Harmonic Analysis in Hypercomplex SystemsFormat:PaperbackDimensions:496 pages, 10.98 × 8.27 × 0 inPublished:December 7, 2010Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048150221

ISBN - 13:9789048150229

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Table of Contents

Preface. Introduction. 1: General Theory of Hypercomplex Systems. 1. Fundamental Concepts of the Theory of Hypercomplex Systems with Locally Compact Basis. 2. Hypercomplex Systems and Related Objects. 3. Elements of Harmonic Analysis for Normal Hypercomplex Systems with Basis Unity. 4. Hypercomplex Subsystems and Homomorphisms. 5. Further Generalizations of Hypercomplex Systems. 2: Examples of Hypercomplex Systems. 1. Centers of Group Algebras of Compact Groups. 2. Gelfand Pairs. 3. Orthogonal Polynomials. 4. Hypercomplex Systems Constructed for the Sturm-Liouville Equation. 3: Elements of Lie Theory for Generalized Translation Operators. 1. Basic Concepts. 2. Analog of Lie Theory for Some Classes of Generalized Translation Operators. 3. Duality of Generators of One-Dimensional Compact and Discrete Hypercomplex Systems. Supplement: Hypercomplex Systems and Hypergroups: Connections and Distinctions. Bibliographical Notes. References. Subject Index.