ENGLISH

Harmonic Analysis of Probability Measures on Hypergroups

By Walter R. Bloom; Herbert Heyer

Book information

Publisher
de Gruyter
Year
1994
ISBN
9783110877595, 9783110121056
Language
english
Format
PDF
Filesize
70 MB (73805301 bytes)
Series
De Gruyter Studies in Mathematics; 20
Pages
607\608
Time added
2023-06-01 01:23:54

Description

Introduction 1 Hypergroups and their measure algebras 1.1 Definition and general constructions 1.2 Translation and convolution 1.3 Invariant measures 1.4 Convolution of functions 1.5 Subhypergroups and double coset hypergroups 1.6 Idempotent measures and multipliers Notes 2 The dual of a commutative hypergroup 2.1 Representations and Fourier transforms 2.2 The dual space in the commutative case 2.3 Modification of the convolution 2.4 The dual hypergroup 2.5 Support of the Plancherel measure Notes 3 Some special classes of hypergroups 3.1 Polynomial hypergroups in several variables 3.2 Polynomial hypergroups in one variable 3.3 Examples of polynomial hypergroups in one variable 3.4 One-dimensional hypergroups 3.5 Sturm-Liouville hypergroups 3.6 Characterization of Pontryagin hypergroups Notes 4 Positive and negative definite functions and measures 4.1 Positive definite functions 4.2 The Lévy continuity theorem 4.3 Positive definite measures 4.4 Negative definite functions 4.5 The Lévy-Khintchine representation Notes 5 Convolution semigroups and divisibility of measures 5.1 Convergence of nets of measures 5.2 Convolution semigroups of measures 5.3 Embedding infinitely divisible measures 5.4 Factorization on hermitian hypergroups Notes 6 Transience of convolution semigroups 6.1 The dichotomy theorem for random walks 6.2 The generalized Chung-Fuchs criterion 6.3 Transience and renewal of convolution semigroups 6.4 Characterization of potential measures 6.5 Invariant Dirichlet forms Notes 7 Randomized sums of hypergroup-valued random variables 7.1 Concretization of hypergroups 7.2 Moment functions 7.3 Strong laws of large numbers 7.4 Central limit theorems 7.5 Invariance principles Notes 8 Further topics 8.1 Towards a structure theory for hypergroups 8.2 Towards a theory of stationary random fields over hypergroups Bibliography Examples Symbols Index

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