Agler interpolation families of kernels
Michael Jury, Greg Knese, Scott McCullough
TL;DR
This paper formulates an abstract Pick interpolation theorem for families of positive semi-definite kernels, extending existing results and enabling applications to Pick interpolation on distinguished varieties.
Contribution
It introduces a new abstract interpolation theorem for kernel families, expanding theoretical tools for complex analysis and operator theory.
Findings
Provides an abstract Pick interpolation theorem for kernel families
Complements existing theorems in the literature
Enables applications to distinguished varieties
Abstract
An abstract Pick interpolation theorem for a family of positive semi-definite kernels on a set is formulated. The result complements those in \cite{Ag} and \cite{AMbook} and will subsequently be applied to Pick interpolation on distinguished varieties \cite{JKM}.
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Taxonomy
TopicsHolomorphic and Operator Theory · Mathematical functions and polynomials · Analytic and geometric function theory