论文标题
$γ$ -Supercyclicity transper transper in Transped $ l^p $ - 当地紧凑的群体上
$Γ$-supercyclicity of families of translates in weighted $L^p$-spaces on locally compact groups
论文作者
论文摘要
让$ω$为本地紧凑的组$ g $，$ 1 \ le p <+\ infty $，$ s \ subset g $定义的权重函数，让我们假设对于任何$ s \ in s $中的任何$ s \，左翻译运营商$ t_s $都是从加权$ l^p $ l^p $ -space $ l^p（g，g，g，g，g，ω）中继续。对于给定的集合$γ\ subset \ mathbb {c} $，如果集合$ \ \ \ \ \ \ {λt_sf：\，λ\，λ\inγ，\ in s \ in s \ in s \ in s \ in s $ l^l^p（g）在本文中，我们表征了$（γ，s）$ - 密度向量，$ l^p（g，ω）$在重量和集合$γ$方面。
Let $ω$ be a weight function defined on a locally compact group $G$, $1\le p<+\infty$, $S\subset G$ and let us assume that for any $s\in S$, the left translation operator $T_s$ is continuous from the weighted $L^p$-space $L^p(G,ω)$ into itself. For a given set $Γ\subset\mathbb{C}$, a vector $f\in L^p(G,ω)$ is said to be $(Γ,S)$-dense if the set $\{ λT_sf:\, λ\in Γ, \,s\in S\}$ is dense in $L^p(G,ω)$. In this paper, we characterize the existence of $(Γ,S)$-dense vectors in $L^p(G,ω)$ in terms of the weight and the set $Γ$.
