Strong asymptotics for Bergman polynomials over domains with corners
arXiv:0910.17881 citations
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This provides a theoretical advance for complex analysis and approximation theory, addressing a long-standing gap for non-smooth domains.
The paper establishes strong asymptotics for Bergman orthogonal polynomials over non-smooth domains with corners, extending previous results for analytic and smooth boundaries from 1923 and the 1960s.
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.