论文标题
分布空间上的可拓扑和功率的加权构图运算符
Topologizable and power bounded weighted composition operators on spaces of distributions
论文作者
论文摘要
我们研究了（某些子空间）$ \ mathscr {d}'（x）$的拓扑性和功率界限，用于开放子集$ x $ of $ \ mathbb {r}^d $。对于以前的属性，我们根据符号和加权构图操作员的重量来得出一个表征，而对于后一种属性，对重量和符号的必要条件和足够的条件。此外，对于未加权的构图操作员，符号的功率界定表征是针对生物符号的特殊情况得出的。
We study topologizability and power boundedness of weigh\-ted composition operators on (certain subspaces of) $\mathscr{D}'(X)$ for an open subset $X$ of $\mathbb{R}^d$. For the former property we derive a characterization in terms of the symbol and the weight of the weighted composition operator, while for the latter property necessary and sufficient conditions on the weight and the symbol are presented. Moreover, for an unweighted composition operator a characterization of power boundedness in terms of the symbol is derived for the special case of a bijective symbol.
