Monomial operators

Jim Agler; John E. McCarthy

doi:10.1007/s44146-022-00021-2

Monomial operators

Jim Agler, John E. McCarthy

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We study monomial operators on L²[0 , 1] , that is bounded linearoperators that map each monomial xⁿ to a multiple of x^pn for some p_n.We show that they are all unitarily equivalent to weighted compositionoperators 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 forboundedness of the operator.

Original language	English
Pages (from-to)	371-381
Number of pages	11
Journal	Acta Scientiarum Mathematicarum
Volume	88
Issue number	1-2
DOIs	https://doi.org/10.1007/s44146-022-00021-2
State	Published - Aug 2022

Keywords

30H10
Carleson measure
weighted composition operator

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10.1007/s44146-022-00021-2

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title = "Monomial operators",

abstract = "We study monomial operators on L2[0 , 1] , that is bounded linearoperators that map each monomial xn to a multiple of xpn for some pn.We show that they are all unitarily equivalent to weighted compositionoperators on a Hardy space. We characterize what sequences pn can arise.In the case that pn is a fixed translation of n, we give a criterion forboundedness of the operator.",

keywords = "30H10, Carleson measure, weighted composition operator",

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note = "Funding Information: Partially supported by National Science Foundation Grant DMS 2054199. Publisher Copyright: {\textcopyright} 2022, University of Szeged.",

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AB - We study monomial operators on L2[0 , 1] , that is bounded linearoperators that map each monomial xn to a multiple of xpn for some pn.We show that they are all unitarily equivalent to weighted compositionoperators on a Hardy space. We characterize what sequences pn can arise.In the case that pn is a fixed translation of n, we give a criterion forboundedness of the operator.

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KW - Carleson measure

KW - weighted composition operator

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JO - Acta Scientiarum Mathematicarum

JF - Acta Scientiarum Mathematicarum

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ER -

Monomial operators

Abstract

Keywords

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