Pick and Peak Interpolation

TL;DR

This paper explores combining Pick and peak interpolation techniques within an abstract uniform algebra framework, extending classical theorems like Rudin-Carleson and Pick interpolation on the disc.

Contribution

It introduces a unified approach to interpolation combining Pick and peak sets in a general algebraic setting, extending classical results.

Findings

Unified interpolation framework in uniform algebras

Extension of Rudin-Carleson theorem with Pick interpolation

Generalization of classical interpolation results

Abstract

We show how Pick interpolation and interpolation on peak interpolation sets can be combined in an abstract uniform algebra setting. In particular as a special case, the Rudin-Carleson theorem can be combined with the classical Pick interpolation theorem on the disc.