Absolute Voronoi summability of Fourier integrals of functions of bounded variation

Author:

Liliya~Boitsun,~Tamara~Rybnikova

2010 Mathematics Subject Classification:

40G05.

Keywords:

Cesaro method, Fourier integral, summability, function of bounded variation, Voronoi method.

Abstract:

In the present paper, we obtain sufficient conditions imposed on the function p(t), under which the Fourier integral of the function f(t)\in L(-\infty,\infty) is absolutely summable by Voronoi method if the function \Phi(t)=f(x+t)+f(x-t)-2f(x) is of bounded variation on (0;+\infty).

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Vol. 10 (18), 2015