UID:
almahu_9947360001202882
Format:
Online-Ressource (vi, 601 p)
Edition:
Online-Ausg. Palo Alto, Calif ebrary 2011 Electronic reproduction; Available via World Wide Web
ISBN:
3110121050 (acid-free paper)
,
9783110121056 (acid-free paper)
,
9783110877595
Series Statement:
De Gruyter studies in mathematics 20
Content:
Harmonic Analysis of Probability Measures on Hypergroups (De Gruyter Studies in Mathematics)
Note:
Includes bibliographical references (p. [553]-580) and index
,
3.1 Polynomial hypergroups in several variables3.2 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 measures5.3 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.
,
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.
,
Notes8 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.
Language:
English
DOI:
10.1515/9783110877595
URL:
http://www.degruyter.com/doi/book/10.1515/9783110877595
