On convergence and estimation of the truncation error of corresponding two-dimensional continued fractions
UDC 517.524For the corresponding two-dimensional continued fractions with complex partial numerators belonging to some subsets of the Cartesian product of two angular sets in the right half-plane and partial denominators equal to one, we establish sufficient conditions of uniform convergence and an...
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| Datum: | 2022 |
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| Hauptverfasser: | , , , , , |
| Format: | Artikel |
| Sprache: | Ukrainisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2022
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/7031 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | UDC 517.524For the corresponding two-dimensional continued fractions with complex partial numerators belonging to some subsets of the Cartesian product of two angular sets in the right half-plane and partial denominators equal to one, we establish sufficient conditions of uniform convergence and an estimation of the truncation error using an analogue of the method of fundamental inequalities, formulas for real and imagine parts of tails of figured approximants and a multidimensional analogue of the Stieltjes-Vitali theorem. |
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| DOI: | 10.37863/umzh.v74i4.7031 |