Convergence of multipoint Padé approximants of piecewise analytic functions

DOI10.1070/SM2013v204n02ABEH004297zbMath1276.41011OpenAlexW2003851036MaRDI QIDQ2842988

Viktor I. Buslaev

Publication date: 9 August 2013

Published in: Sbornik: Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/sm2013v204n02abeh004297

zbMATH Keywords

orthogonal polynomialsPadé approximantsrational approximationconvergence in capacityasymptotic behaviour of poles

Mathematics Subject Classification ID

Padé approximation (41A21) Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions (31A15)

Related Items (11)

On the existence of compacta of minimal capacity in the theory of rational approximation of multi-valued analytic functions ⋮ Convergence of two-point Padé approximants to piecewise holomorphic functions ⋮ Zero distribution for Angelesco Hermite–Padé polynomials ⋮ Numerical analytic continuation ⋮ Capacity of a compact set in a logarithmic potential field ⋮ On equilibrium problems related to the distribution of zeros of the Hermite-Padé polynomials ⋮ Strong asymptotics of two-point Padé approximants for power-like multivalued functions ⋮ The distribution of the zeros of the Hermite-Padé polynomials for a pair of functions forming a Nikishin system ⋮ On a new approach to the problem of distribution of zeros of Hermite-Padé polynomials for a Nikishin system ⋮ On multipoint Padé approximants whose poles accumulate on contours that separate the plane ⋮ On a lower bound for the rate of convergence of multipoint Padé approximants of piecewise analytic functions

Cites Work

• Orthogonal polynomials with complex-valued weight function. I
• Orthogonal polynomials with complex-valued weight function. II
• Convergence of rational interpolants
• Random matrices with external source and the asymptotic behaviour of multiple orthogonal polynomials
• Extremal domains associated with an analytic function I
• Extremal domains associated with an analytic function II
• EQUILIBRIUM DISTRIBUTIONS AND DEGREE OF RATIONAL APPROXIMATION OF ANALYTIC FUNCTIONS
• Padé approximants, continued fractions, and orthogonal polynomials
• Hermite-Padé approximations and multiple orthogonal polynomial ensembles
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