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Thin sequences and the Gram matrix

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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 ≤ ∞.

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Authors and Affiliations

  1. Department of Mathematics, Bucknell University, Lewisburg, PA, 17837, USA

    Pamela Gorkin

  2. Department of Mathematics, Washington University in St. Louis, St. Louis, MO, 63130, USA

    John E. McCarthy

  3. Faculty of Science, Centre for Mathematical Sciences, Lund University, 22100, Lund, Sweden

    Sandra Pott

  4. School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, GA, 30332-0160, USA

    Brett D. Wick

Authors
  1. Pamela Gorkin
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  2. John E. McCarthy
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  3. Sandra Pott
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  4. Brett D. Wick
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Corresponding author

Correspondence to Pamela Gorkin.

Additional 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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Gorkin, P., McCarthy, J.E., Pott, S. et al. Thin sequences and the Gram matrix. Arch. Math. 103, 93–99 (2014). https://doi.org/10.1007/s00013-014-0667-8

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  • DOI: https://doi.org/10.1007/s00013-014-0667-8

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