Thin Sequences and Their Role in Model Spaces and Douglas Algebras

Pamela Gorkin; Brett D. Wick

doi:10.1007/s00041-015-9414-1

Thin Sequences and Their Role in Model Spaces and Douglas Algebras

Pamela Gorkin, Brett D. Wick

Department of Mathematics & Statistics

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

2 Scopus citations

Abstract

We study thin interpolating sequences {λn} and their relationship to interpolation in the Hardy space H² and the model spaces (Formula presented.), where Θ is an inner function. Our results, phrased in terms of the functions that do the interpolation as well as Carleson measures, show that under the assumption that (Formula presented.) the interpolation properties in H² are essentially the same as those in KΘ.

Original language	English
Pages (from-to)	137-158
Number of pages	22
Journal	Journal of Fourier Analysis and Applications
Volume	22
Issue number	1
DOIs	https://doi.org/10.1007/s00041-015-9414-1
State	Published - Feb 1 2016

Keywords

Asymptotic orthonormal sequence
Interpolation
Reproducing kernel
Thin sequences

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abstract = "We study thin interpolating sequences {λn} and their relationship to interpolation in the Hardy space H2 and the model spaces (Formula presented.), where Θ is an inner function. Our results, phrased in terms of the functions that do the interpolation as well as Carleson measures, show that under the assumption that (Formula presented.) the interpolation properties in H2 are essentially the same as those in KΘ.",

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AB - We study thin interpolating sequences {λn} and their relationship to interpolation in the Hardy space H2 and the model spaces (Formula presented.), where Θ is an inner function. Our results, phrased in terms of the functions that do the interpolation as well as Carleson measures, show that under the assumption that (Formula presented.) the interpolation properties in H2 are essentially the same as those in KΘ.

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KW - Interpolation

KW - Reproducing kernel

KW - Thin sequences

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Thin Sequences and Their Role in Model Spaces and Douglas Algebras

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Keywords

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