On summability of subsequences of partial sums of trigonometric Fourier series

1991 ◽  
Vol 17 (4) ◽  
pp. 281-295
Author(s):  
D. V. Leladze
Keyword(s):  
Fourier Series ◽  
Trigonometric Fourier Series ◽  
Partial Sums

Trigonometric Fourier series and Walsh-Fourier series with lacunary sequence of partial sums

2013 ◽  
Vol 93 (1-2) ◽  
pp. 332-336
Author(s):  
S. K. Bloshanskaya ◽  
I. L. Bloshanskii ◽  
O. V. Lifantseva
Keyword(s):  
Fourier Series ◽  
Lacunary Sequence ◽  
Trigonometric Fourier Series ◽  
Partial Sums

scholarly journals Approximation of the function |sin x| s by the partial sums of the trigonmometric rational fourier series

2021 ◽  
Vol 65 (1) ◽  
pp. 11-17
Author(s):  
N. Yu. Kazlouskaya ◽  
Ya. A. Rovba
Keyword(s):  
Fourier Series ◽  
Integral Representation ◽  
Present Article ◽  
Asymptotic Equality ◽  
Fixed Number ◽  
Trigonometric Fourier Series ◽  
Partial Sums ◽  
Point Estimates ◽  
Special Cases ◽  
Selection Of

In the present article, the approximation of the function |sin x| s by the partial sums of the rational trigonometric Fourier series is considered. An integral representation, uniform and point estimates for the above-mentioned approximation were obtained. Based on them, several special cases of the selection of poles were studied. In the case of the approximation by the partial sums of the polynomial trigonometric Fourier series, an asymptotic equality was found. A detailed study is made of a fixed number of geometrically different poles.

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