Open AccessOn degree of approximation of non-periodic function by Voronoi means of its Fourier integral
Author(s) -
L.G. Bojtsun,
A.O. Deordiieva
Publication year - 2021
Publication title -
researches in mathematics
Language(s) - English
Resource type - Journals
eISSN - 2664-5009
pISSN - 2664-4991
DOI - 10.15421/241103
Subject(s) - voronoi diagram , degree (music) , fourier transform , fourier series , mathematics , function (biology) , mathematical analysis , fourier analysis , combinatorics , physics , geometry , evolutionary biology , acoustics , biology
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.