Growth behavior and zero distribution of rational approximants

DOI10.1007/S00365-010-9124-5zbMath1236.41014OpenAlexW2057558981MaRDI QIDQ662814

Ralitza K. Kovacheva, Hans-Peter Blatt

Publication date: 13 February 2012

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00365-010-9124-5

zbMATH Keywords

Padé approximationrational approximationdistribution of zerosharmonic majorants\(m_1\)-maximal convergenceJentzsch-Szegő-type theorems

Mathematics Subject Classification ID

Approximation in the complex plane (30E10) Approximation by rational functions (41A20) Padé approximation (41A21) Rate of convergence, degree of approximation (41A25) Real rational functions (26C15)

Related Items (10)

Growth Behavior and Zero Distribution of Maximally Convergent Rational Approximants ⋮ On overconvergence of closed to row subsequences of classical Padé approximants ⋮ Overconvergence of Rational Approximants of Meromorphic Functions ⋮ Zero distribution of incomplete Padé and Hermite-Padé approximations ⋮ Exact maximal convergence in capacity and zero distribution of rational approximants ⋮ On the distribution of zeros and poles of rational approximants on intervals ⋮ The Jentzsch-Szegő theorem and balayage measures ⋮ Distribution of interpolation points of maximally convergent multipoint Padé approximants ⋮ A note on the explicit asymptotics of rows and of closed to row sequences of classical Padé approximants ⋮ Rate of convergence of row sequences of multipoint Padé approximants

Cites Work

• The analogue for maximally convergent polynomials of Jentzsch's theorem
• Behavior of zeros of polynomials of near best approximation
• Poles and alternation points in real rational Chebyshev approximation
• On the zeros of sequences of polynomials
• Overconvergence, degree of convergence and zeros of sequences of analytic functions
• Jentzsch-Szegö Type Theorems for the Zeros of Best Approximants
• Regions of Meromorphy Determined by the Degree of Best Rational Approximation
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