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On conjugate rational trigonometric Fourier series and their approximation properties
N. Ju. Kazlouskaya, Y. A. Rovba Yanka Kupala State University of Grodno
Abstract:
The article considers conjugate rational trigonometric Fourier series. An integral representation of their partial sums and the Dini test for the convergence of the given series were obtained. The approximation of functions conjugate to $|\sin x|^s$, $s>0$ by partial sums of conjugate rational trigonometric Fourier series is investigated. An integral representation, uniform and point estimates for the above-mentioned approximation were obtained. On the base of the uniform estimate polynomial, a fixed number of geometrically different poles, and general cases were studied.
Received: 15.02.2023
Citation:
N. Ju. Kazlouskaya, Y. A. Rovba, “On conjugate rational trigonometric Fourier series and their approximation properties”, Tr. Inst. Mat., 31:1 (2023), 58–69
Linking options:
https://www.mathnet.ru/eng/timb362 https://www.mathnet.ru/eng/timb/v31/i1/p58
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Abstract page: | 63 | Full-text PDF : | 28 | References: | 15 |
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