%0 Journal Article
%A Raisi Tousi, R.
%A Esmaeelzadeh, F.
%A Kamyabi Gol, R. A.
%T The Representations and Positive Type Functions of Some Homogenous Spaces
%J Iranian Journal of Mathematical Sciences and Informatics
%V 11
%N 1
%U http://ijmsi.ir/article-1-482-en.html
%R 10.7508/ijmsi.2016.01.005
%D 2016
%K Homogenous space, Semidirect product, Convolution, Involution, Representation, Irreducible representation.,
%X For a homogeneous spaces $G/H$, we show that the convolution on $L^1(G/H)$ 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 between nondegenerat $ast$-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.
%> http://ijmsi.ir/article-1-482-en.pdf
%P 47-56
%& 47
%!
%9 Research paper
%L A-10-538-1
%+ Bojnourd Branch, Islamic Azad University
%G eng
%@ 1735-4463
%[ 2016