Some remarks about interpolating sequences in reproducing kernel Hilbert spaces

TL;DR

This paper investigates interpolation problems in reproducing kernel Hilbert spaces, providing new equivalences for conditions on interpolating sequences on Riemann surfaces and the polydisc, enhancing understanding of these mathematical structures.

Contribution

It introduces new equivalences for interpolation conditions on Riemann surfaces and the polydisc within reproducing kernel Hilbert spaces, expanding theoretical understanding.

Findings

New equivalences for Stout's Theorem on Riemann surfaces

Characterizations of interpolation in the Schur-Agler class

Conditions for interpolation in reproducing kernel Hilbert spaces

Abstract

In this paper we study two separate problems on interpolation. We first give some new equivalences of Stout's Theorem on necessary and sufficient conditions for a sequence of points to be an interpolating sequence on a finite open Riemann surface. We next turn our attention to the question of interpolation for reproducing kernel Hilbert spaces on the polydisc and provide a collection of equivalent statements about when it is possible to interpolation in the Schur-Agler class of the associated reproducing kernel Hilbert space.