Harmonic Analysis of Probability Measures on Hypergroups
1st Edition
Published on 20. April 2011
VI, 601 pages
978-3-11-087759-5 (ISBN)
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Walter R. Bloom | Herbert Heyer
Harmonic Analysis of Probability Measures on Hypergroups
Book
01/1995
1st Edition
De Gruyter
€309.00
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Walter R. Bloom | Herbert Heyer
Harmonic Analysis of Probability Measures on Hypergroups
Book
11/1994
1st Edition
De Gruyter
€220.00
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Content
- Intro
- 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
