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

References


Bojtsun L.G. "On absolute summability of conjugate Fourier integrals by method of Voronoi", Izv. vuzov. Matematika, 1967; 6: pp. 11-21. (in Russian)

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)

Voronoi G.F. Extension of concept of infinite series sum limit. In: Sobr. soch. in 3 vol., Kyiv, 1952; 3: pp. 9-10. (in Russian)

Titchmarsh E.C. Introduction to the theory of Fourier integral, Moscow, 1948; 479 p. (in Russian)

Fikhtengolts G.M. Course on integral and differential calculus. Vol. 2, Moscow, 1959. (in Russian)

Nörlund N.E. "Sur une application des fonctions permutables", Junds Univ. Arsskrift(2), 1919; 16(3): pp. 1-10. (in French)




DOI: https://doi.org/10.15421/241103

  

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ISSN (Print): 2664-4991
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