An analog of Gonchar's theorem for the \(m\)-point version of Leighton's conjecture

DOI10.1134/S008154381604009XzbMath1367.30004WikidataQ122904602 ScholiaQ122904602MaRDI QIDQ338491

Viktor I. Buslaev

Publication date: 7 November 2016

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

zbMATH Keywords

continued fractionconvergence of continued fractionLeighton's conjecture

Mathematics Subject Classification ID

Continued fractions (11A55) Continued fractions; complex-analytic aspects (30B70) Convergence and divergence of continued fractions (40A15)

Related Items (8)

Continued fractions with limit periodic coefficients ⋮ An analog of Pólya's theorem for multivalued analytic functions with finitely many branch points ⋮ On the Van Vleck theorem for limit-periodic continued fractions of general form ⋮ Necessary and sufficient conditions for extending a function to a Schur function ⋮ The capacity of the rational preimage of a compact set ⋮ On singular points of meromorphic functions determined by continued fractions ⋮ On a new approach to the problem of distribution of zeros of Hermite-Padé polynomials for a Nikishin system ⋮ Schur’s criterion for formal power series

Cites Work

• On the existence of compacta of minimal capacity in the theory of rational approximation of multi-valued analytic functions
• Capacity of a compact set in a logarithmic potential field
• On equilibrium problems related to the distribution of zeros of the Hermite-Padé polynomials
• The convergence of Padé approximants to functions with branch points
• An estimate of the capacity of singular sets of functions that are defined by continued fractions
• Continued fraction expansions for arbitrary power series
• An analogue of Polya's theorem for piecewise holomorphic functions
• Distribution of the zeros of Padé polynomials and analytic continuation
• Convergence of m-point Padé approximants of a tuple of multivalued analytic functions
• Singular Points of Functions Defined by C-Fractions
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