N-strongly quasi-invariant measure on double coset spaces

Document Type : Research Paper


1 Department of Mathematics, Center of Excellecy in Analysis on Algebric Structures (CEAAS), Ferdowsi University of Mashhad, Mashhad, Iran

2 Department of Mathematics, Bojnourd Branch, Islamic Azad university, Bojnourd, Iran



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. 


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