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Thin sequences and the Gram matrix |
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| Authors: | Pamela Gorkin John E. McCarthy Sandra Pott Brett D. Wick |
| Affiliation: | 1. Department of Mathematics, Bucknell University, Lewisburg, PA, 17837, USA 2. Department of Mathematics, Washington University in St. Louis, St. Louis, MO, 63130, USA 3. Faculty of Science, Centre for Mathematical Sciences, Lund University, 22100, Lund, Sweden 4. School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, GA, 30332-0160, USA |
| 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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