Alexander P. Schuster

Finite unions of interpolation sequences

A unified and relatively simple proof is given for some well-known results involving finite unions of uniformly separated sequences.

Sets of sampling and interpolation in Bergman spaces

Properties of the unions of sampling and interpolation sets for Bergman spaces are discussed in conjunction with the examples given by Seip [9]. Their relationship to the classical interpolation sequences is explored. In addition, the role played by canonical divisors in the study of these sets is examined and an example of a sampling set is constructed in the disk. §

WEAK CONDITIONS FOR INTERPOLATION IN HOLOMORPHIC SPACES

An analogue of the notion of uniformly separated sequences, expressed in terms of extremal functions, yields a necessary and sufficient condition for interpolation in Lp spaces of holomorphic functions of Paley-Wiener-type when

The maximum principle for the Bergman space and the Möbius pseudodistance for the annulus

0 < p \leq 1

Uniform densities of regular sequences in the unit disk

, of Fock-type when

On seip's description of sampling sequences for bergman spaces

0 < p \leq 2

Interpolation and Sampling for Generalized Bergman Spaces on finite Riemann surfaces

, and of Bergman-type when

Multiple interpolation and extremal functions in the Bergman spaces

0 < p < \infty

Sampling Sequences for Bergman Spaces for p < 1

. Moreover, if a uniformly discrete sequence has a certain uniform non-uniqueness property with respect to any such Lp space (

Toeplitz Operators and Carleson Measures on Generalized Bargmann–Fock Spaces

0 < p < \infty