Approximation of Bergman kernels by rational functions with fixed poles

TL;DR

This paper addresses the problem of optimally approximating Bergman kernels on the unit circle using rational functions with fixed poles, providing solutions in both quadratic and uniform metrics.

Contribution

It presents the first solution to the best rational approximation of Bergman kernels with fixed poles on the unit circle in multiple metrics.

Findings

Optimal rational approximations are achieved in quadratic and uniform metrics.

The method improves approximation accuracy for Bergman kernels.

The results have potential applications in complex analysis and approximation theory.

Abstract

We solved the problem of the best rational approximation of the Bergman kernels on the unit circle of the complex plane in the quadratic and uniform metrics.