On conjugate rational trigonometric Fourier series and their approximation properties
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.
About the Authors
N. Ju. Kazlouskaya
Yanka Kupala State University of Grodna
Belarus
Belarus
Ya. A. Rovba
Yanka Kupala State University of Grodna
Belarus
Belarus
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Review
For citations:
Kazlouskaya N.J., Rovba Ya.A. On conjugate rational trigonometric Fourier series and their approximation properties. Trudy Instituta matematiki. 2023;31(1):58-69. (In Russ.)
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