Thin sequences and the Gram matrix
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 p is greater than or equal to 2 (including infinity).
Gorkin, Pamela; McCarthy, John E.; Pott, Sandra; and Wick, Brett. "Thin sequences and the Gram matrix." Archiv Math. 103, no. 1 (2014) : 93-99.