%0 Journal Article %T N-strongly quasi-invariant measure on double coset spaces %J Wavelet and Linear Algebra %I Vali-e-Asr university of Rafsanjan %Z 2383-1936 %A Fahimian, Fatemeh %A Kamyabi Gol, Rajab Ali %A Esmaeelzadeh, Fatemeh %D 2022 %\ 11/01/2022 %V 9 %N 1 %P 67-84 %! N-strongly quasi-invariant measure on double coset spaces %K Double coset space %K $N$-Strongly quasi invariant measure %K rho-function %R 10.22072/wala.2022.550186.1370 %X Let $G$ be a locally compact group, $H$ and $K$ be two closed subgroups of $G$, and $N$ be the normalizer group of $K$ in $G$. In this paper, the existence and properties of a rho-function for the triple $(K, G, H)$ and an $N$-strongly quasi-invariant measure of double coset space $K \backslash G /H$ is investigated. In particular, it is shown that any such measure arises from a rho-function. Furthermore, the conditions under which an $N$-strongly quasi-invariant measure arises from a rho-function are studied.  %U https://wala.vru.ac.ir/article_698482_eb0b55dc660364225d2ae4732c709657.pdf