Originally Published In
Gorkin, Pamela; McCarthy, John E.; Pott, Sandra; Wick, Brett D.; Thin sequences and the Gram matrix. Arch. Math. (Basel) 103 (2014), no. 1, 93–99.
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≤∞.
Gorkin, Pamela; McCarthy, John E.; Pott, Sandra; and Wick, Brett D., "Thin sequences and the Gram matrix" (2014). Mathematics Faculty Publications. 15.