A NOTE ON '-GELFAND PAIRS

In this paper, at rst, concept of '-Gelfand pairs is de ned,where ' is an endomorphism of locally compact group G such that '(K) K. (K is a compact subgroup of G). Then its properties is studied, especially,whether the Gelfand pairs theorems, holds for '-Gelfand pairs ischaracterized. Also some of the equivalent conditions for '-Gelfand pairs islooked at, and representations of class one with respect to ' is introduced.Finally a sketch of the harmonic analysis for '-Gelfand pairs and compact'-Gelfand pairs is presented

کلیدواژه ها:

-Gelfand pair ، bi-'(K)-invariant measure ، locally compactgroup ، character ، '-spherical function ، Gelfand pairs