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Sibirskii Matematicheskii Zhurnal, 2012, Volume 53, Number 5, Pages 1027–1047
(Mi smj2328)
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This article is cited in 2 scientific papers (total in 2 papers)
Interpolation of analytic functions with finitely many singularities
A. G. Lipchinskiĭ P. P. Ershov Ishim State Pedagogical Institute, Ishim, Tyumen reg.
Abstract:
We consider an interpolation process for the class of functions with finitely many singular points by means of rational functions whose poles coincide with the singular points of the function under interpolation. The interpolation nodes form a triangular matrix. We find necessary and sufficient conditions for the uniform convergence of sequences of interpolation fractions to the function under interpolation on every compact set disjoint from the singular points of the function and other conditions for convergence. We generalize and improve the familiar results on the interpolation of functions with finitely many singular points by rational fractions and of entire functions by polynomials.
Keywords:
analytic function, singularity of a function, interpolation process, rational fraction, uniform convergence, convergence conditions.
Received: 12.04.2011
Citation:
A. G. Lipchinskiǐ, “Interpolation of analytic functions with finitely many singularities”, Sibirsk. Mat. Zh., 53:5 (2012), 1027–1047; Siberian Math. J., 53:5 (2012), 821–838
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https://www.mathnet.ru/eng/smj2328 https://www.mathnet.ru/eng/smj/v53/i5/p1027
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Abstract page: | 257 | Full-text PDF : | 88 | References: | 49 | First page: | 1 |
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