Mathematics

Some properties of transformed Fourier series

B. V. Simonov


Abstract: 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.

UDC: 517.51

Received: 12.05.1982

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