Monomial Operators

2022/05/04 by Agler, Jim, McCarthy, John E.
#46E22 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2205.01857

Abstract

We study monomial operators on L²[0,1], that is bounded linear operators that map each monomial xⁿ 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.

Related

• Boundedness and compactness of weighted composition operators and monomial operators
• A generalization of Hardy's operator and an asymptotic Muntz-Szasz Theorem
• Characterization of weighted Hardy spaces on which all composition operators are bounded
• Beurling's theorem for the Hardy operator on L²[0,1]
• New equivalence theorems for weighted inequalities involving the composition of monotone quasilinear operators with the Hardy and Copson operators and their applications