Iranian Journal of Mathematical Sciences and Informatics, Volume (1), No (1), Year (2016-1) , Pages (1-1)
Title : ( The representations and positive type functions of some homogenous spaces )
Authors: Reihaneh Raisi Tousi , F. Esmaeelzadeh , Rajab Ali Kamyabi Gol ,
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Abstract
For a homogeneous spaces G=H, we show that the convo- lution on L1(G=H) is the same as convolution on L1(K), where G is semidirect product of a closed subgroup H and a normal subgroup K of G. Also we prove that there exists a one to one correspondence be- tween nondegenerat -representations of L1(G=H) and representations of G=H. We propose a relation between cyclic representations of L1(G=H) and positive type functions on G=H. We prove that the Gelfand Raikov theorem for G=H holds if and only if H is normal.
