A Class of Functional Equations on a Locally Compact Group |
| |
Authors: | Akkouchi, Mohamed Bakali, Allal Khalil, Idriss |
| |
Affiliation: | Bab Doukkala (R'mila) Derb el Ferrane 9, 40.000 Marrakech, Morocco Département de Mathématiques, Faculté des Sciences, Université Ibn Tofail Kenitra, Morocco Département de Mathématiques, Faculté des Sciences, Université Mohammed V Rabat, Morocco |
| |
Abstract: | Let G be a locally compact group not necessarily unimodular.Let µ be a regular and bounded measure on G. We study,in this paper, the following integral equation, E(µ) This equation generalizes the functional equation for sphericalfunctions on a Gel'fand pair. We seek solutions in the spaceof continuous and bounded functions on G. If is a continuousunitary representation of G such that (µ) is of rank one,then tr((µ)(x)) is a solution of E(µ). (Here, trmeans trace). We give some conditions under which all solutionsare of that form. We show that E(µ) has (bounded and)integrable solutions if and only if G admits integrable, irreducibleand continuous unitary representations. We solve completelythe problem when G is compact. This paper contains also a listof results dealing with general aspects of E(µ) and propertiesof its solutions. We treat examples and give some applications. |
| |
Keywords: | |
本文献已被 Oxford 等数据库收录! |
|