A generalization of Hardy's operator and an asymptotic Muntz-Szasz Theorem

2022/05/04 by Agler, Jim, McCarthy, John E. · 1 citation
#41A10 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2205.01856

Abstract

The Hardy operator has all the monomial functions as eigenvectors. We study bounded operators on L² 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.

Cited by

• On Markushevich bases \x^λ_n\_n=1^∞ for their closed span in weighted L² (A) spaces over sets A⊂ [0,∞) of positive Lebesgue measure, hereditary completeness, and moment problems

Related

• Asymptotic Muntz-Szasz Theorems
• Monomial Operators
• Beurling's theorem for the Hardy operator on L²[0,1]
• Asymptotic properties for a general class of Szasz-Mirakjan-Durrmeyer operators
• Conditions for Boundedness into Hardy spaces