On one criterion for the figured convergence of two-dimensional continued fractions with complex elements

We establish a new criterion for the figured convergence of two-dimensional continued fractions with complex elements. This criterion represents a generalization of the theorems of simple and twin convergence sets for continued fractions.

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2010-11, Vol.170 (5), p.594-603
Main Authors: Antonova, T. M., Sus’, O. M.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Description
Summary:We establish a new criterion for the figured convergence of two-dimensional continued fractions with complex elements. This criterion represents a generalization of the theorems of simple and twin convergence sets for continued fractions.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-010-0104-x