Interpolating Sequences in Spaces with the Complete Pick Property

Alexandru Aleman; Michael Hartz; John E. McCarthy; Stefan Richter

doi:10.1093/imrn/rnx237

Interpolating Sequences in Spaces with the Complete Pick Property

Alexandru Aleman, Michael Hartz, John E. McCarthy, Stefan Richter

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

25 Scopus citations

Abstract

We characterize interpolating sequences for multiplier algebras of spaces with the complete Pick property. Specifically, we show that a sequence is interpolating if and only if it is separated and generates a Carleson measure. This generalizes results of Carleson for the Hardy space and of Bishop, Marshall, and Sundberg for the Dirichlet space. Furthermore, we investigate interpolating sequences for pairs of Hilbert function spaces.

Original language	English
Pages (from-to)	3832-3854
Number of pages	23
Journal	International Mathematics Research Notices
Volume	2019
Issue number	12
DOIs	https://doi.org/10.1093/imrn/rnx237
State	Published - Jun 18 2019

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title = "Interpolating Sequences in Spaces with the Complete Pick Property",

abstract = "We characterize interpolating sequences for multiplier algebras of spaces with the complete Pick property. Specifically, we show that a sequence is interpolating if and only if it is separated and generates a Carleson measure. This generalizes results of Carleson for the Hardy space and of Bishop, Marshall, and Sundberg for the Dirichlet space. Furthermore, we investigate interpolating sequences for pairs of Hilbert function spaces.",

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AU - Richter, Stefan

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N2 - We characterize interpolating sequences for multiplier algebras of spaces with the complete Pick property. Specifically, we show that a sequence is interpolating if and only if it is separated and generates a Carleson measure. This generalizes results of Carleson for the Hardy space and of Bishop, Marshall, and Sundberg for the Dirichlet space. Furthermore, we investigate interpolating sequences for pairs of Hilbert function spaces.

AB - We characterize interpolating sequences for multiplier algebras of spaces with the complete Pick property. Specifically, we show that a sequence is interpolating if and only if it is separated and generates a Carleson measure. This generalizes results of Carleson for the Hardy space and of Bishop, Marshall, and Sundberg for the Dirichlet space. Furthermore, we investigate interpolating sequences for pairs of Hilbert function spaces.

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U2 - 10.1093/imrn/rnx237

DO - 10.1093/imrn/rnx237

M3 - Article

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VL - 2019

SP - 3832

EP - 3854

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 12

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Interpolating Sequences in Spaces with the Complete Pick Property

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