Zero distributions for polynomials orthogonal with weights over certain planar regions

DOI10.1007/BF03321094zbMath1098.30009OpenAlexW1980599843MaRDI QIDQ816263

Edward B. Saff, Erwin Miña-Díaz, Nikos S. Stylianopoulos

Publication date: 10 March 2006

Published in: Computational Methods and Function Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf03321094

zbMATH Keywords

orthogonal polynomialszeros of polynomialskernel functionequilibrium measurelogarithmic potential

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in two dimensions (31A05) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Polynomials and rational functions of one complex variable (30C10) Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions (31A15) Kernel functions in one complex variable and applications (30C40)

Related Items (13)

Asymptotics of Carleman polynomials for level curves of the inverse of a shifted Zhukovsky transformation ⋮ Relative asymptotics of orthogonal polynomials for perturbed measures ⋮ Asymptotic behavior and zero distribution of Carleman orthogonal polynomials ⋮ Lemniscate growth ⋮ Bergman orthogonal polynomials on an archipelago ⋮ Asymptotics for polynomial zeros: Beware of predictions from plots ⋮ Christoffel functions on curves and domains ⋮ On new class of linear and positive operators ⋮ On the zeros of asymptotically extremal polynomial sequences in the plane ⋮ Universality type limits for Bergman orthogonal polynomials ⋮ Bergman polynomials on an archipelago: estimates, zeros and shape reconstruction ⋮ Asymptotics of polynomials orthogonal over circular multiply connected domains ⋮ Error analysis of the Bergman kernel method with singular basis functions

Cites Work

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• Asymptotic behaviour of zeros of Bieberbach polynomials
• Zero distribution of Bergman orthogonal polynomials for certain planar domains
• Zeros of polynomials orthogonal over regular \(N\)-gons.
• Weighted mean square approximation in plane regions, and generators of an algebra of analytic functions
• On the distribution of zeros of polynomials orthogonal on the unit circle
• Overconvergence, degree of convergence and zeros of sequences of analytic functions
• Weighted Mean Approximation in Carathéodory Regions.
• On the completeness of systems of analytic functions

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