Geodesic
On conjugate rational trigonometric Fourier series and their approximation properties
Trudy Instituta matematiki, Tome 31 (2023) no. 1, pp. 58-69 
N. Ju. Kazlouskaya; Y. A. Rovba. On conjugate rational trigonometric Fourier series and their approximation properties. Trudy Instituta matematiki, Tome 31 (2023) no. 1, pp. 58-69. http://geodesic.mathdoc.fr/item/TIMB_2023_31_1_a7/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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