论文标题
维也纳定理的矢量有价值的代数类似物
Vector valued Beurling algebra analogues of Wiener's Theorem
论文作者
论文摘要
令$ 0 <p \ leq 1 $，$ω$是$ \ mathbb z $的重量，让$ \ m rathcal a $为Unital Banach代数。如果$ f $是单位圆$ \ mathbb t $到$ \ mathcal a $的连续函数，以至于$ \ sum_ {n \ in \ mathbb z} \ | \ | \ widehat f（n）\ |^p（n）\ |^pΩ（n）\ |^pω（n）^p <\ in） $ \ MATHBB Z $和连续函数$ g：\ Mathbb t \ to \ Mathcal a $，以至于$ 1 \ leq leq leqleqν\ leqleqΩ$，$ν$在且仅当$ω$是常数时，$ g $是$ g $，$ g $是$ f $ $ f $ and $ f $ and $ \ sum_ {n \ in \ sum_ { g（n）\ |^pν（n）^p <\ infty $。当$ω$是几乎单调的代数重量和$ 1 <p <\ infty $时，我们将获得类似的结果。我们将在实际线路上获得此结果的类似物。我们将应用这些结果来获得$ p- $ Power加权的类似物的偏对矩阵的对角线衰减的结果。
Let $0<p\leq 1$, $ω$ be a weight on $\mathbb Z$, and let $\mathcal A$ be a unital Banach algebra. If $f$ is a continuous function from the unit circle $\mathbb T$ to $\mathcal A$ such that $\sum_{n\in \mathbb Z} \|\widehat f(n)\|^p ω(n)^p<\infty$ and $f(z)$ is left invertible for all $z \in \mathbb T$, then there is a weight $ν$ on $\mathbb Z$ and a continuous function $g:\mathbb T \to \mathcal A$ such that $1\leq ν\leq ω$, $ν$ is constant if and only if $ω$ is constant, $g$ is a left inverse of $f$ and $\sum_{n\in \mathbb Z}\|\widehat g(n)\|^pν(n)^p<\infty$. We shall obtain a similar result when $ω$ is an almost monotone algebra weight and $1<p<\infty$. We shall obtain an analogue of this result on the real line. We shall apply these results to obtain $p-$power weighted analogues of the results of off diagonal decay of infinite matrices of operators.
