On degree of approximation of non-periodic function by Voronoi means of its Fourier integral

L.G. Bojtsun; A.O. Deordiieva

doi:10.15421/241103

On degree of approximation of non-periodic function by Voronoi means of its Fourier integral

L.G. Bojtsun (Oles Honchar Dnipropetrovsk National University)
A.O. Deordiieva (Oles Honchar Dnipropetrovsk National University)

Abstract

The theorem on the degree of approximation to a function $$$f(x) \in L(-\infty; \infty)$$$ by Voronoi means of its Fourier integral, as well as a theorem on the degree of approximation to a function $$$g(x) = \frac{1}{\pi} \int\limits_0^{\infty} \frac{f(x+t) - f(x-t)}{t} dt$$$ by the Voronoi means of its conjugate Fourier integral of a function $$$f(x)$$$, is proved.

Keywords

approximation to a function; the Voronoi means; Fourier integral

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References

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Bojtsun L.G., Rybnikova T.I. "On degree of approximation of function by Cesaro means of its Fourier integral", Researches on modern problems of summation and approximation of functions and their applications, DGU, 1975; 5: pp. 16-23. (in Russian)

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