About relationship between summability of almost periodic functions and Fouriers coefficients

Khasanov, Yu. Kh.
Vladikavkaz Mathematical Journal 2014. Vol. 16. Issue 3.

Abstract:
We generalize Paley's theorem for Bezicovich and Stepanov almost periodic functions on arbitrary trigonometric system. It is proved that for any trigonometric
series under some conditions there exists an almost-periodic function which  the given series is its Fourier series.

Keywords: almost periodic functions, Fourier series, Fourier coefficients, relationship summability, series convergence

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