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

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].

Spherical functions for Gelfand pairs associated with compact groupoids

2015 ◽  
Vol 27 (3-4) ◽  
pp. 573-582
Author(s):  
Ibrahima Toure ◽  
Kinvi Kangni
Keyword(s):  
Spherical Functions ◽  
Gelfand Pairs

scholarly journals Superstability of functional equations related to spherical functions

2017 ◽  
Vol 15 (1) ◽  
pp. 427-432 ◽  
Author(s):  
László Székelyhidi
Keyword(s):  
Functional Equations ◽  
Spherical Functions ◽  
Invariant Means ◽  
Stability Type

Abstract In this paper we prove stability-type theorems for functional equations related to spherical functions. Our proofs are based on superstability-type methods and on the method of invariant means.

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

1982 ◽  
Vol 14 (2) ◽  
pp. 272-294 ◽  
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.

scholarly journals Gelfand pairs and spherical functions

1979 ◽  
Vol 2 (2) ◽  
pp. 153-162 ◽  
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.

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

1982 ◽  
Vol 14 (02) ◽  
pp. 272-294 ◽  
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.

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