Continued fractions with limit periodic coefficients

Continued fractions with limit periodic coefficients

The boundary properties of functions represented by limit periodic continued fractions of a fairly general form are investigated. Such functions are shown to have no single-valued meromorphic extension to any neighbourhood of any non-isolated boundary point of the set of convergence of the continued...

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Veröffentlicht in:Sbornik. Mathematics 2018-02, Vol.209 (2), p.187-205
1. Verfasser: Buslaev, V. I.
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Sprache:eng
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continued fractions
Hankel determinants
meromorphic extension
transfinite diameter
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creator Buslaev, V. I.
description The boundary properties of functions represented by limit periodic continued fractions of a fairly general form are investigated. Such functions are shown to have no single-valued meromorphic extension to any neighbourhood of any non-isolated boundary point of the set of convergence of the continued fraction. The boundary of the set of meromorphy has the property of symmetry in an external field determined by the parameters of the continued fraction. Bibliography: 26 titles.
doi_str_mv 10.1070/SM8687
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source IOP Publishing Journals; Alma/SFX Local Collection
subjects continued fractions
Hankel determinants
meromorphic extension
transfinite diameter
title Continued fractions with limit periodic coefficients
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