On the Van Vleck theorem for limit-periodic continued fractions of general form
type: Item
instance of: scholarly article
title: On the Van Vleck theorem for limit-periodic continued fractions of general form
zbMATH Open document ID: 1394.30001
DOI: 10.1134/S0081543817060062
published in: Proceedings of the Steklov Institute of Mathematics
publication date: 2018-02-27T00:00:00Z
review text: Let \(A_1(z)/(B_1(z)+A_2(z)/(B_2(z)+ \cdots))\) be a continued fraction. Here the sequence of polynomials \(\{A_n\}_{n=1}^{\infty}\) has periodic limits with zeros lying on a finite set \(E\), and the sequence of polynomials \(\{B_n\}_{n=1}^{\infty}\) has periodic limits with zeros lying outside \(E\). The boundary of the convergence domain of the continued fraction is established. It is shown that the functions defined by continued fractions do not have a single-valued meromorphic continuation to any neighborhood of any nonisolated point of the boundary of the convergence set. The main theorem of the paper is a generalization of the Van Vleck theorem and Gonchar's complement to the Van Vleck theorem.
reviewed by: Mykhaylo Pahirya
Mathematics Subject Classification ID: 30B70
Mathematics Subject Classification ID: 40A15
zbMATH DE Number: 6844176
zbMATH Keywords: continued fractions
zbMATH Keywords: limit-periodic continued fractions
zbMATH Keywords: Van Vleck theorem
zbMATH Keywords: convergence set
author: Viktor I. Buslaev
MaRDI profile type: Publication
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full work available at URL: s0081543817060062
OpenAlex ID: W2769353358
description: scientific article; zbMATH DE number 6844176