Monomial operators

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(pn) 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.

Automated summary

This article studies monomial operators on L-2[0, 1] and their properties. It proves their equivalence to weighted composition operators on the Hardy space and characterizes the possible sequences p(n). In the case where p(n) is a fixed translation of n, a criterion for boundedness of the operator is provided.