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Here is the story as I see it. Let $G$ be an abelian locally compact group. Then the (spherical) Hecke algebra for $K=1$ is by definition the endomorphism algebra of $l^2(G)$ as a $G$-module, where ...

I'm looking for references about the following aspect of cyclic vectors for regular representations. Let $K$ be a compact Lie group. Let $K$ act on $L^2(K)$ by the left regular representation. Then $...

For a Lie group $G$ and a locally convex space $V$ let $\mathcal{E}(G,V)$ be the locally convex space of smooth functions from $G$ to $V$, and accordingly $\mathcal{E}_c^\prime(G,V)$ the space of ...

Consider a representation $A$ of a group $G$ in a complex vector space ${\mathbb{V}}$: $$ A:~~G~\longrightarrow~\operatorname{GL}({\mathbb{V}})~~, $$ and let ${\mathbb{V}}$ be decomposable into a ...

I am reading the paper [Margulis, G. A.; Nevo, A.; Stein, E. M., Analogs of Wiener's ergodic theorems for semisimple Lie groups. II. Duke Math. J. 103 (2000), no. 2, 233–259] (MSN). I want to ...

Consider a Hilbert space $\mathcal{H}$ which is a carrier space of a unitary, irreducible and strongly continuous representation $\Pi$ of a Lie group $G$. Let $\Pi\otimes \Pi$ denote the corresponding ...