Some remarks about interpolating sequences in reproducing kernel Hilbert spaces

Details Some remarks about interpolating sequences in reproducing kernel Hilbert spaces Some remarks about interpolating sequences in reproducing kernel Hilbert spaces

2011-09-08

arxiv.org/abs/1109.1857v1

Mathematics

Functional Analysis

14 pages, no figures

Scientific paper

In this paper we study two separate problems on interpolation. We first give a new proof of Stout's Theorem on necessary and sufficient conditions for a sequence of points to be an interpolating sequence for the multiplier algebra and for an associated Hilbert space. 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.

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