Nevanlinna-Pick interpolation on distinguished varieties in the bidisk

TL;DR

This paper explores Nevanlinna-Pick interpolation on distinguished varieties in the bidisk, providing an interpolation theorem and operator theoretic results using reproducing kernels, with examples like Neil parabola and doubly connected domains.

Contribution

It introduces a new interpolation theorem and operator results specific to distinguished varieties, expanding the understanding of interpolation in complex analysis.

Findings

Interpolation theorem for distinguished varieties

Operator theoretic results using reproducing kernels

Applications to Neil parabola and doubly connected domains

Abstract

This article treats Nevanlinna-Pick interpolation in the setting of a special class of algebraic curves called distinguished varieties. An interpolation theorem, along with additional operator theoretic results, is given using a family of reproducing kernels naturally associated to the variety. The examples of the Neil parabola and doubly connected domains are discussed.