One-component bounded functions
Carlo Bellavita, Artur Nicolau
TL;DR
This paper provides three distinct characterizations of one-component bounded analytic functions, linking factorization, kernel size, and measure-theoretic properties to deepen understanding of their structure.
Contribution
It introduces new characterizations of one-component bounded functions, connecting factorization, reproducing kernels, and Clark measures in a unified framework.
Findings
Characterization via inner-outer factorization
Reproducing kernel size criteria in de Branges-Rovnyak spaces
Clark measure properties related to one-component functions
Abstract
Three different characterizations of one-component bounded analytic functions are provided. The first one is related to the the inner-outer factorization, the second one is in terms of the size of the reproducing kernels in the corresponding de Branges-Rovnyak spaces and the last one concerns the associated Clark measure.
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Taxonomy
TopicsApproximation Theory and Sequence Spaces · Advanced Banach Space Theory · Holomorphic and Operator Theory