Work

Maximal Convergence of Fourier Series with Respect to Bergman Orthogonal Polynomials via Their Strong Asymptotics

Year: 2026

Type: article

Abstract: Let G⊂C be a bounded simply connected domain with rectifiable Jordan boundary. Denote by ϕ the conformal map of the exterior of G onto the exterior of the unit disk. For R>1, let ΓR be the level curve defined by ϕ(z)=R, and let GR denote its interior, so that G⊂GR. Suppose that f is analytic in GR. In this paper, we investigate the maximal convergence properties of the Fourier series of f with respect to the Bergman orthogonal polynomials of G. By employing the strong asymptotics of Bergman polynomials outside the domain G of orthogonality, determined by the boundary properties of G, we obtain estimates for the maximal convergence rate of the partial sums of the Fourier series of f in the uniform norm on G¯. These estimates are expressed in terms of the best polynomial approximation of f in the domain GR where f is analytic.

Source: Axioms

DOI: 10.3390/axioms15050326

Author: Burçin Oktay

Institution: Balıkesir University

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: Balikesir Üniversitesi