Summation of trigonometric Fourier integrals by method of G.F. Voronoi

In this paper we establish sufficient conditions of summability, by functional method of G.F. Voronoi, of Fourier integral of a function $f(t) \in L_{(-\infty, \infty)}$.

Absolute summability of conjugate Fourier integrals by Voronoi-Nerlund method

We establish conditions of absolute summability of Fourier integrals and conjugate Fourier integrals by Voronoi-Nerlund method.

Absolute summation of Fourier integrals with multiplier by G.F. Voronoi method

We provide the theorem that is connected with functional method of G.F. Voronoi. We establish sufficient conditions for a function that generates the summation method of G.F. Voronoi, on function-multiplier, and on function $f(t)$, under which the Fourier integral of this function with multiplier is absolutely summable by the functional method of G.F. Voronoi.

Absolute convergence of Fourier integrals and Lipschitz classes

The necessary and sufficient conditions, in terms of Fourier transforms $\hat{f}$ of functions $f \in L^1(\mathbb{R})$, are obtained for $f$ to belong to the Lipschitz classes $H^{\omega}(\mathbb{R})$ and $h^{\omega}(\mathbb{R})$.