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

Mathematics (Faculty of Sciences)

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

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 <= infinity.

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

Subject classification (UKÄ)

Mathematical Sciences

Free keywords

Gram matrix
Thin interpolating sequence
Schatten-p class

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10.1007/s00013-014-0667-8

Cite this

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AU - Gorkin, Pamela

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AU - Pott, Sandra

AU - Wick, Brett D.

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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 <= infinity.

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 <= infinity.

KW - Gram matrix

KW - Thin interpolating sequence

KW - Schatten-p class

UR - https://www.scopus.com/pages/publications/84905489807

U2 - 10.1007/s00013-014-0667-8

DO - 10.1007/s00013-014-0667-8

M3 - Article

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

Abstract

Subject classification (UKÄ)

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