AU - Raisi Tousi, R.
AU - Esmaeelzadeh, F.
AU - Kamyabi Gol, R. A.
TI - The Representations and Positive Type Functions of Some Homogenous Spaces
PT - JOURNAL ARTICLE
TA - IJMSI
JN - IJMSI
VO - 11
VI - 1
IP - 1
4099 - http://ijmsi.ir/article-1-482-en.html
4100 - http://ijmsi.ir/article-1-482-en.pdf
SO - IJMSI 1
ABĀ - 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.
CP - IRAN
IN -
LG - eng
PB - IJMSI
PG - 47
PT - Research paper
YR - 2016