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题名/责任者:

Harmonic analysis on hypergroups : approximation and stochastic sequences / Rupert Lasser, Technical University of Munich, Germany.

出版发行项:

New Jersey : World Scientific, [2023]

ISBN:

9789811266195

载体形态项:

xviii, 602 pages ; 24 cm.

丛编说明:

Series on multivariate analysis, 1793-1169 ; vol. 14

个人责任者:

Lasser, Rupert, 1948- author.

论题主题:

Harmonic analysis.

论题主题:

Hypergroups.

中图法分类号:

O177.55

书目附注:

Includes bibliographical references (pages 559-596) and index.

摘要附注:

"The book aims at giving a monographic presentation of the abstract harmonic analysis of hypergroups, while combining it with applied topics of spectral analysis, approximation by orthogonal expansions and stochastic sequences. Hypergroups are locally compact Hausdorff spaces equipped with a convolution, an involution and a unit element. Related algebraic structures had already been studied by Frobenius around 1900. Their axiomatic characterisation in harmonic analysis was later developed in the 1970s. Hypergoups naturally emerge in seemingly different application areas as time series analysis, probability theory and theoretical physics. The book presents harmonic analysis on commutative and polynomial hypergroups as well as weakly stationary random fields and sequences thereon. For polynomial hypergroups also difference equations and stationary sequences are considered. At greater extent than in the existing literature, the book compiles a rather comprehensive list of hypergroups, in particular of polynomial hypergroups. With an eye on readers at advanced undergraduate and graduate level, the proofs are generally worked out in careful detail. The bibliography is extensive"--

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