Geodesic
Some properties of transformed Fourier series
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (1983), pp. 58-61

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We find some conditions under which the transformed Fourier series of a function $f(x)\in L_p$ is a Fourier series of a suitable function $\varphi(x)\in L_p$. We also find some estimates of the module of smoothness of the fractional order for the function $\varphi(x)$. We study the precision of these estimates. 
@article{VMUMM_1983_2_a12,
     author = {B. V. Simonov},
     title = {Some properties of transformed {Fourier} series},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {58--61},
     publisher = {mathdoc},
     number = {2},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_1983_2_a12/}
}
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B. V. Simonov. Some properties of transformed Fourier series. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (1983), pp. 58-61. http://geodesic.mathdoc.fr/item/VMUMM_1983_2_a12/