All Questions

I recently meet the following two weird "Fourier transform" questions. (I), Suppose that $F$ is a $p$-adic field (the same question can be asked over any local field, including $\mathbb{R}$ ...

Let $G$ be a locally compact group and $\Gamma$ a lattice in $G$. For an irreducible unitary representation $\pi$ of $G$ let $$ m_\Gamma(\pi)=\dim\mathrm{Hom}_G(\pi,L^2(\Gamma\backslash G)) $$ be its ...

Following Bernstein-Zelevinski, an $\ell$-space is a Hausdorff, locally compact totally disconnected topological space. For an $\ell$-space $X$, denote $S(X)$ the space of Bruhat-Schwartz functions on ...

Dear all, I have some difficulty in understanding the notion of automorphic forms on product of groups. Let $G$, $H$ be two reductive groups defined over a number field $F$. Let $\mathcal{A}(G)$ be ...

In obtaining the spectral decomposition of $L^2(\Gamma \backslash G)$ where $G=SL_2(\mathbb{R})$, and $\Gamma$ is an arithmetic subgroup (I am satisfied with $\Gamma = SL (2,\mathbb{Z})$) we have a ...