Effective H^{\infty} interpolation

TL;DR

This paper investigates optimal interpolation of holomorphic functions within the unit disk, focusing on minimizing norms in a smaller function class while matching given data points.

Contribution

It introduces a method for effective H^{} interpolation between function classes, optimizing norm minimization under data constraints.

Findings

Derived bounds for interpolation norms.

Established existence and uniqueness of optimal interpolants.

Provided explicit construction methods for the interpolating functions.

Abstract

Given a finite set \sigma of the unit disc \mathbb{D}={z\in\mathbb{C}:, |z|<1} and a holomorphic function f in \mathbb{D} which belongs to a class X, we are looking for a function g in another class Y (smaller than X) which minimizes the norm |g|_{Y} among all functions g such that g_{|\sigma}=f_{|\sigma}.