Harmonic analysis in hypercomplex systems /
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...
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| Format: | eBook |
| Language: | English |
| Published: |
Dordrecht ; Boston :
Kluwer Academic,
[1998]
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| Series: | Mathematics and its applications (Kluwer Academic Publishers) ;
volume 434. |
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| Online Access: | Connect to the full text of this electronic book |
| Summary: | 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. |
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| Physical Description: | 1 online resource (x, 483 pages) : illustrations. |
| Bibliography: | Includes bibliographical references (pages 439-479) and index. |
| ISBN: | 9789401717588 (electronic bk.) 9401717583 (electronic bk.) |