A generalization of Hardy's operator and an asymptotic Muntz-Szasz Theorem
Functional Analysis
2022-05-05 v1
Abstract
The Hardy operator has all the monomial functions as eigenvectors. We study bounded operators on L^2 that take monomial functions to multiples of other monomials, with a shifted exponent. We prove that they all leave the space of functions vanishing on [0,s] invariant. We prove an asymptotic Muntz-Szasz theorem, characterizing the set of functions that are limits of linear combinations of monomials with exponents between n and 2n.
Keywords
Cite
@article{arxiv.2205.01856,
title = {A generalization of Hardy's operator and an asymptotic Muntz-Szasz Theorem},
author = {Jim Agler and John E. McCarthy},
journal= {arXiv preprint arXiv:2205.01856},
year = {2022}
}