Convolution semigroups and central limit theorem associated with a dual convolution structure

DOI10.1007/BF02214276zbMath0796.60010MaRDI QIDQ1322915

Néjib Ben Salem

Publication date: 20 September 1994

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

zbMATH Keywords

Fourier transformshyperbolic spacesLevy-Khinchin formulaJacobi hypergroupGaussian limit distributionsSturm-Liouville hypergroup structure

Mathematics Subject Classification ID

Harmonic analysis on hypergroups (43A62) Convergence of probability measures (60B10) Applications of hypergeometric functions (33C90) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

Related Items (6)

On the fractional Bessel operator ⋮ Mehler integral transform associated with Jacobi functions with respect to the dual variable ⋮ Integral representations of pseudo-differential operator associated with the Jacobi differential operator ⋮ Hypoelliptic Jacobi convolution operators on Schwartz distributions ⋮ Pseudo-differential operators associated with the Jacobi differential operator ⋮ Pseudo-differential operators associated with the Jacobi differential operator and Fourier-cosine wavelet transform

Cites Work

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• Convolution semigroups of probability measures on Gelfand pairs
• Convolution semigroups on hypergroups
• One-dimensional hypergroups
• On the Fourier transformation of positive, positive definite measures on commutative hypergroups, and dual convolution structures
• On the dual space of a commutative hypergroup
• Spaces with an abstract convolution of measures
• Jacobi functions: the addition formula and the positivity of the dual convolution structure
• The central limit theorem for Chébli-Trimèche hypergroups
• Paley-Wiener type theorems for a differential operator connected with symmetric spaces
• The convolution structure for Jacobi function expansions
• Positive Definite and Related Functions on Hypergroups

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