Thin sequences and the Gram matrix

Pamela Gorkin; John E. McCarthy; Sandra Pott; Brett D. Wick

doi:10.1007/s00013-014-0667-8

Thin sequences and the Gram matrix

Pamela Gorkin, John E. McCarthy, Sandra Pott, Brett D. Wick

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

6 Scopus citations

Abstract

We provide a new proof of Volberg's Theorem characterizing thin interpolating sequences as those for which the Gram matrix associated to the normalized reproducing kernels is a compact perturbation of the identity. In the same paper, Volberg characterized sequences for which the Gram matrix is a compact perturbation of a unitary as well as those for which the Gram matrix is a Schatten-2 class perturbation of a unitary operator. We extend this characterization from 2 to p, where 2 ≤ p ≤ ∞.

Original language	English
Pages (from-to)	93-99
Number of pages	7
Journal	Archiv der Mathematik
Volume	103
Issue number	1
DOIs	https://doi.org/10.1007/s00013-014-0667-8
State	Published - Jul 2014

Keywords

Gram matrix
Schatten-p class
Thin interpolating sequence

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10.1007/s00013-014-0667-8

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title = "Thin sequences and the Gram matrix",

abstract = "We provide a new proof of Volberg's Theorem characterizing thin interpolating sequences as those for which the Gram matrix associated to the normalized reproducing kernels is a compact perturbation of the identity. In the same paper, Volberg characterized sequences for which the Gram matrix is a compact perturbation of a unitary as well as those for which the Gram matrix is a Schatten-2 class perturbation of a unitary operator. We extend this characterization from 2 to p, where 2 ≤ p ≤ ∞.",

keywords = "Gram matrix, Schatten-p class, Thin interpolating sequence",

author = "Pamela Gorkin and McCarthy, {John E.} and Sandra Pott and Wick, {Brett D.}",

note = "Funding Information: P.G. Partially supported by Simons Foundation Grant 243653. J.M. Partially supported by National Science Foundation Grant DMS 1300280. B.D.W Partially supported by National Science Foundation Grant DMS 0955432.",

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AU - Gorkin, Pamela

AU - McCarthy, John E.

AU - Pott, Sandra

AU - Wick, Brett D.

N1 - Funding Information: P.G. Partially supported by Simons Foundation Grant 243653. J.M. Partially supported by National Science Foundation Grant DMS 1300280. B.D.W Partially supported by National Science Foundation Grant DMS 0955432.

PY - 2014/7

Y1 - 2014/7

N2 - We provide a new proof of Volberg's Theorem characterizing thin interpolating sequences as those for which the Gram matrix associated to the normalized reproducing kernels is a compact perturbation of the identity. In the same paper, Volberg characterized sequences for which the Gram matrix is a compact perturbation of a unitary as well as those for which the Gram matrix is a Schatten-2 class perturbation of a unitary operator. We extend this characterization from 2 to p, where 2 ≤ p ≤ ∞.

AB - We provide a new proof of Volberg's Theorem characterizing thin interpolating sequences as those for which the Gram matrix associated to the normalized reproducing kernels is a compact perturbation of the identity. In the same paper, Volberg characterized sequences for which the Gram matrix is a compact perturbation of a unitary as well as those for which the Gram matrix is a Schatten-2 class perturbation of a unitary operator. We extend this characterization from 2 to p, where 2 ≤ p ≤ ∞.

KW - Gram matrix

KW - Schatten-p class

KW - Thin interpolating sequence

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DO - 10.1007/s00013-014-0667-8

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SN - 0003-889X

VL - 103

SP - 93

EP - 99

JO - Archiv der Mathematik

JF - Archiv der Mathematik

IS - 1

ER -

Thin sequences and the Gram matrix

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Keywords

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