Ph.D Thesis Defense: "Interpolating Matrices"

Abstract: We extend Carleson Interpolating Theorem to sequences of matrices in the unit disc. This will be done by analyzing separation conditions on model sub-spaces of the Hardy space, and by relating such conditions to the notion of separated and interpolating matrices. We will also introduce and characterize interpolating sequences of d-tuples of matrices in terms of a quasi-orthogonality conditions for related reproducing kernel Hilbert spaces. The commutative and the noncommutative case will be analyzed separately, although the techniques used are similar. Specifically, we will extend Agler’s and McCarthy’s characterization of interpolating sequences in the bi-disc to pairs of commuting matrices, while for the noncommutative case we will refer to an analogous of the Pick property for the noncommutative Drury-Arveson space.

Host: John McCarthy