Fourier-Stieltjes Transforms on Hypergroups

Lasser, Rupert

doi:10.1524/anly.1982.2.14.281

Cited by 11 publications

(3 citation statements)

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“…Properties of the convolution operator Τ μ defined by for all / of appropriate spaces of functions have been studied and exposed in [40] and [24]. Occasionally we shall also consider Τ μ for arbitrary measures μ e M+(K) which involves convolvability of measures μ, ν e M+(K).…”

Section: T X F(y):= I F(z)e X * E Y (Dz) Jkmentioning

confidence: 99%

Convolution semigroups and potential kernels on a commutative hypergroup

Heyer¹

1990

The Analytical and Topological Theory of Semigroups

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The aim of this expose is to survey recent advances in the potential theory of convolution semigroups on a commutative hypergroup. The problems to be discussed are related to the theory of space-homogeneous Markov processes on a commutative hypergroup. Their solutions are achieved by an application of harmonic analysis of commutative hypergroups. Some of the topics that will be covered in this paper arose from open questions posed in the author's previous survey [32]. The remarkable contributions of the last five years to the Schoenberg correspondence, the transience and embedding problems seem to make it worthwhile to once again look into the state of the art with curiosity. The reader will recognize that part of the theory presented here developed from the desire of extending the main theorems of the monograph [6] of C. BERG and G. FORST from Abelian locally compact groups to commutative hypergroups. In In the process, obstacles had to be overcome and at the same time new phenomena had to be envisaged. Both aspects are the motives for the author to collaborate with WALTER R. BLOOM on a book on probabilities and potentials on a hypergroup. The present survey can be considered as a synopsis for a central section of that book.The author has profited from still unpublished work of M. VOIT and H. ZEUNER. Preliminaries on commutative hypergroupsFor a locally compact space K we introduce the system R(K) of all compact subsets of K furnished with the Michael topology. By %) X (K) we abbreviate the system of open neighborhoods of χ in K. The symbols C b (K), C°(K) and /C(/Q denote the spaces of bounded continuous functions on K, continuous functions on Κ vanishing at infinity, and continuous functions on Κ having compact support. C b (K) will carry the compact open topology T co . The inclusions M\K) C M W (K) C M b (K) C M(K) concern the sets of probability measures, contraction measures (measures of norm < 1), bounded measures and arbitrary (Radon) measures on K. In λΛ(Κ) we consider the vague topology T v , Unauthenticated Download Date | 6/15/16 7:09 PM

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Section: T X F(y):= I F(z)e X * E Y (Dz) Jkmentioning

confidence: 99%

Convolution semigroups and potential kernels on a commutative hypergroup

Heyer¹

1990

The Analytical and Topological Theory of Semigroups

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“…[7, 25, 27, 37, 511 55, 56, 65, 66, 90, 97, 98, 106, 134, 136, 145]), expansions in orthogonal systems of functions and special functions (cf. [2,7,51,55,56,114,131,136,[142][143][144]183]), spectral decomposition of operators (cf. [3,5,51,55,56,135,149,150,178]), duality theory (cf.…”

Section: 5mentioning

confidence: 99%

Hypergroups and hypergroup algebras

Litvinov¹

1987

J Math Sci

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“…[9]) or in orthogonal polynomial sequences (see [12]). Many topics, which are classic for harmonic analysis on groups, have been investigated on hypergroups, such as spectral synthesis ( [2]), invariant measures ( [17]) and Fourier--Stieltjes transforms ( [11]), to mention only a few.…”

Section: Introductionmentioning

confidence: 99%

Weakly almost periodic functions on hypergroups

Wolfenstetter

1983

Monatshefte f�r Mathematik

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Abstract.The results about weakly almost periodic functions on topological groups can only partly be transferred to the case of hypergroups. The main achievements of this paper are the construction of a bounded continuous, but not w. a. p. function (which is in this generality even new for groups) and the result that WAP(K) is not an algebra in general. Finally we compare "classical" w.a.p. functions on [FIA]~-groups with those on the orbit space G ~.

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Fourier-Stieltjes Transforms on Hypergroups

Abstract: For commutative hypergroups Κ there are given various criterions characterizing the Fourier-Stieltjes transforms among the functions on the dual K. These results are applied to solve some expansion problems with respect to orthogonal polynomial sequences.

Cited by 11 publications

References 11 publications

Convolution semigroups and potential kernels on a commutative hypergroup

Convolution semigroups and potential kernels on a commutative hypergroup

Hypergroups and hypergroup algebras

Weakly almost periodic functions on hypergroups

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