Mrinal Raghupathi
Some remarks about interpolating sequences in reproducing kernel Hilbert spaces.
Mon, 09/12/2011 - 15:01 — SomNambulAuthors: Brett D. Wick, Mrinal Raghupathi
Subjects: Functional Analysis
AbstractIn 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.Duality, Tangential Interpolation, and Toeplitz Corona Problems.
Mon, 12/14/2009 - 16:01 — SomNambulAuthors: Brett D. Wick, Mrinal Raghupathi
Subjects: Functional Analysis
AbstractIn this paper we extend a method of Arveson and McCullough to prove a
tangential interpolation theorem for subalgebras of $H^\infty$. This tangential
interpolation result implies a Toelitz corona theorem. In particular, it is
shown that the set of matrix positivity conditions is indexed by cyclic
subspaces, which is analogous to the results obtained for the ball and the
polydisk algebra by Trent-Wick and Douglas-Sarkar.
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