The Representations and Positive Type Functions of Some Homogenous Spaces

For a homogeneous spaces G=H, we show that the convolution on L61(G=H) is the same as convolution on L^1(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 L^1(G=H) and representations of G=H. We propose a relation between cyclic representations of L^1(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.