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This article is cited in 3 scientific papers (total in 3 papers)
Research Papers
Vallee Poussin sums of rational Fourier–Chebyshev integral operators and approximations of the Markov function
P. G. Potseiko, Y. A. Rovba Yanka Kupala State University of Grodno
Abstract:
Rational approximations on the segment $[–1, 1]$ of the Markov function are studied. The Vallee Poussin sums of rational integral
Fourier–Chebyshev operators as an approximation apparatus with a fixed number of geometrically distinct poles are chosen. For the constructed rational approximation method, integral representations of approximations and upper estimates of uniform approximations are established.
For a Markov function with a measure whose derivative there is a function that has a power-law singularity on the segment $[–1, 1]$, upper estimates of pointwise and uniform approximations and asymptotic expression of the majorant of uniform approximations are found. The values of the parameters of the approximating function are determined, at which the best uniform rational approximations are provided by this method. It is shown that in this case they have a higher rate of decrease in comparison with the corresponding polynomial analogues.
As a corollary, rational approximations on a segment by Vallee Poussin sums of some elementary functions representable by a Markov function are considered.
Keywords:
Markov function, rational integral operators, de la Vall?e-Poussin sums, uniform rational approximations, asymptotic estimates, Laplace method.
Received: 08.12.2022
Citation:
P. G. Potseiko, Y. A. Rovba, “Vallee Poussin sums of rational Fourier–Chebyshev integral operators and approximations of the Markov function”, Algebra i Analiz, 35:5 (2023), 183–208; St. Petersburg Math. J., 35:5 (2024), 879–896
Linking options:
https://www.mathnet.ru/eng/aa1888 https://www.mathnet.ru/eng/aa/v35/i5/p183
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Abstract page: | 114 | Full-text PDF : | 10 | References: | 25 | First page: | 15 |
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