The Szego curve, zero distribution and weighted approximation

DOI10.1090/S0002-9947-97-01889-8zbMath1114.30312OpenAlexW1592884692MaRDI QIDQ4372571

Richard S. Varga, Igor E. Pritsker

Publication date: 16 December 1997

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-97-01889-8

zbMATH Keywords

balayageSzegő curvelogarithmic potentialextremal measureweighted polynomialsweighted energy problemmodified Robin constant

Mathematics Subject Classification ID

Approximation in the complex plane (30E10) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Approximation by other special function classes (41A30) Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions (31A15)

Related Items (12)

On the zero attractor of the Euler polynomials ⋮ Angular distribution of zeros of the partial sums of \(e^z\) via the solution of inverse logarithmic potential problem ⋮ Approximation by Bernstein–Faber–Walsh and Szász–Mirakjan–Faber–Walsh Operators in Multiply Connected Compact Sets of ℂ $$\mathbb{C}$$ ⋮ Quadratic differentials and asymptotics of Laguerre polynomials with varying complex parameters ⋮ The Szegő curve and Laguerre polynomials with large negative parameters ⋮ A DISCRETE QUEUE, FOURIER SAMPLING ON SZEGÖ CURVES AND SPITZER FORMULAS ⋮ Incomplete beta polynomials ⋮ Pathologies of the large-\(N\) limit for \(\mathbb{RP}^{N-1}\), \(\mathbb{CP}^{N-1}\), \(\mathbb{QP}^{N-1}\) and mixed isovector/isotensor \(\sigma\)-models ⋮ Real zeroes of random analytic functions associated with geometries of constant curvature ⋮ Recursion relations for chromatic coefficients for graphs and hypergraphs ⋮ Riemann-Hilbert analysis for Laguerre polynomials with large negative parameter. ⋮ Weighted rational approximation in the complex plane

Cites Work

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• Asymptotics for the zeros of the partial sums of \(e^ z\). I
• The distribution of zeros of asymptotically extremal polynomials
• Weighted analogues of capacity, transfinite diameter, and Chebyshev constant
• Weighted approximation with varying weight
• Incomplete rational approximation in the complex plane
• A Characterization of the Exponential Series

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