Generating functions for the spherical functions on some classical Gelfand pairs

After an elementary description of Gelfand pairs, spherical functions and Plancherel measure, some explicit computations on the related Markov chains are performed. Random walks on polyhedra belong to this class of Markov chains; two more examples of chains on graphs are worked out, and the necessary and sufficient condition of transcience of random walks on p-adic numbers with spherical symmetry is given as an application of the techniques of the paper.

Download Full-text

Gelfand pairs and spherical functions

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171279000168 ◽

1979 ◽

Vol 2 (2) ◽

pp. 153-162 ◽

Cited By ~ 5

Author(s):

Jean Dieudonné

Keyword(s):

Lie Groups ◽

Special Functions ◽

American Mathematical Society ◽

Linear Representation ◽

Spherical Functions ◽

Mathematical Society ◽

Gelfand Pairs ◽

Research Conference ◽

East Carolina University

This is a summary of the lectures delivered on Special Functions and Linear Representation of Lie Groups at the NSF-CBMS Research Conference at East Carolina University in March 5-9, 1979. The entire lectures will be published by the American Mathematical Society as a conference monograph in Mathematics.

Download Full-text

Les fonctions sphériques d'un couple de Gelfand symétrique et les chaînes de Markov

Advances in Applied Probability ◽

10.1017/s0001867800020449 ◽

1982 ◽

Vol 14 (02) ◽

pp. 272-294 ◽

Cited By ~ 3

Author(s):

Gérard Letac

Keyword(s):

Markov Chains ◽

Random Walks ◽

Spherical Symmetry ◽

Spherical Functions ◽

Plancherel Measure ◽

Sufficient Condition ◽

Gelfand Pairs ◽

Necessary And Sufficient Condition ◽

Necessary And Sufficient

After an elementary description of Gelfand pairs, spherical functions and Plancherel measure, some explicit computations on the related Markov chains are performed. Random walks on polyhedra belong to this class of Markov chains; two more examples of chains on graphs are worked out, and the necessary and sufficient condition of transcience of random walks on p-adic numbers with spherical symmetry is given as an application of the techniques of the paper.

Download Full-text

Gelfand Pairs and Generalized d'Alembert's and Cauchy's Functional Equations

Georgian Mathematical Journal ◽

10.1515/gmj.2005.207 ◽

2005 ◽

Vol 12 (2) ◽

pp. 207-216

Author(s):

Belaid Bouikhalene ◽

Samir Kabbaj

Keyword(s):

Functional Equations ◽

Spherical Functions ◽

Aequationes Math ◽

Gelfand Pairs

Abstract We show that Cauchy's, d'Alembert's functional equations and their generalizations are the functional equations for bounded spherical functions associated to some Gel'fand pairs. Our results are very close to the ones obtained by Stetkær in [Aequationes Math. 48: 220–227, 1994].

Download Full-text