论文标题
单一操作员
Monomial Operators
论文作者
论文摘要
我们在$ l^2 [0,1] $上研究单一操作员，这是有界的线性操作员，每个单元$ x^n $映射到$ x^{p_n} $的倍数，对于某些$ p_n $。我们表明它们在耐寒空间上都与加权构图运算符相当。我们表征哪些序列$ p_n $可能会出现。如果$ p_n $是$ n $的固定翻译，我们给出了操作员有限的标准。
We study monomial operators on $ L^2[0,1]$, that is bounded linear operators that map each monomial $x^n$ to a multiple of $x^{p_n}$ for some $p_n$. We show that they are all unitarily equivalent to weighted composition operators on a Hardy space. We characterize what sequences $p_n$ can arise. In the case that $p_n$ is a fixed translation of $n$, we give a criterion for boundedness of the operator.
