Strong asymptotics for Bergman polynomials over domains with corners

TL;DR

This paper derives strong asymptotic formulas for Bergman polynomials over non-smooth domains, extending classical results from smooth and analytic boundary cases to domains with corners in the complex plane.

Contribution

It provides the first strong asymptotic results for Bergman polynomials on domains with corners, filling a gap in the classical theory.

Findings

Established strong asymptotics for Bergman polynomials on domains with corners.

Extended classical asymptotic results from smooth to non-smooth boundary domains.

Complements previous work on analytic and smooth boundary domains.

Abstract

The aim of the paper is to establish the strong asymptotics for the Bergman orthogonal polynomials defined over non-smooth domains in the complex plane. This complements an investigation started in 1923 by T. Carleman, who derived the strong asymptotics for domains with analytic boundaries and carried over by P.K. Suetin in the 1960's, who established them for domains with smooth boundaries.