TY - JOUR
T1 - The Representations and Positive Type Functions of Some Homogenous Spaces
TT -
JF - IJMSI
JO - IJMSI
VL - 11
IS - 1
UR - http://ijmsi.ir/article-1-482-en.html
Y1 - 2016
SP - 47
EP - 56
KW - Homogenous space
KW - Semidirect product
KW - Convolution
KW - Involution
KW - Representation
KW - Irreducible representation.
N2 - 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.
M3 10.7508/ijmsi.2016.01.005
ER -