Covariant Functions of Characters of Compact Subgroups

Banach Convolution Modules of Group Algebras on Covariant Functions of Characters of Normal Subgroups

This paper investigates structure of Banach convolution modules induced by group algebras on covariant functions of characters of closed normal subgroups. Let $G$ be a locally compact group with the group algebra $L^1(G)$ and $N$ be a closed normal subgroup of $G$. Suppose that $ξ:N\to\mathbb{T}$ is a continuous character, $1\le p<\infty$ and $L_ξ^p(G,N)$ is the $L^p$-space of all covariant functions of $ξ$ on $G$. It is shown that $L^p_ξ(G,N)$ is a Banach $L^1(G)$-module. We then study convolution module actions of group algebras on covariant functions of characters for the case of canonical …

Harmonic Analysis of Covariant Functions of Characters of Normal Subgroups

Let $G$ be a locally compact group with the group algebra $L^1(G)$ and $N$ be a closed normal subgroup of $G$. Suppose that $ξ:N\to\mathbb{T}$ is a continuous character and $L_ξ^1(G,N)$ is the $L^1$-space of all covariant functions of $ξ$ on $G$. We showed that $L^1_ξ(G,N)$ is isometrically isomorphic to a quotient space of $L^1(G)$. It is also proved that the dual space $L^1_ξ(G,N)^*$ is isometrically isomorphic to $L^\infty_ξ(G,N)$.

正规子群不变特征标的协变函数代数

Covariant Function Algebras of Invariant Characters of Normal Subgroups

本文建立局部紧群闭正规子群不变特征标协变函数空间的卷积代数与 Banach 模理论，并推广到半直积群及示例。

$\rm{SL}(n)$ covariant function-valued valuations

Classifications of $\rm{SL}(n)$ covariant function-valued valuations are established with some assumptions of continuity. New valuations, for example, weighted moment functions, are introduced and our classifications give unified characterizations of the Laplace transform on convex bodies, $L_p$ moment bodies, $L_p$ difference bodies, and polar $L_p$ moment bodies ($L_{-p}$ intersection bodies). Using the new classifications, we also establish some Euler-type relations.

The Zak transform and representations induced from characters of an abelian subgroup

We consider a variant of the Zak transform for a finite group $G$ with respect to a fixed abelian subgroup $H$, and demonstrate a relationship with representations of $G$ induced from characters of $H$. We also show how the Zak transform can be used to study right translations by $H$ in $L^2(G)$, and give some examples of applications for equiangular tight frames.