On degree of approximation of function by Voronoi means of its Fourier integral

L.G. Bojtsun (Oles Honchar Dnipropetrovsk National University)
T.I. Rybnikova (Oles Honchar Dnipropetrovsk National University)

Abstract


The theorem on the degree of approximation to continuous function $$$f(x) \in L(-\infty; \infty)$$$ by Voronoi means of its Fourier integral is proved.

Keywords


approximation to a function; the Voronoi means; Fourier integral

References


Flett T.M. "On the degree of approximation to a function by the Cesaro means of its Fourier series", Quart. J. Math., 1956; 7(1): pp. 81-95. doi:10.1093/qmath/7.1.81

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

Saxena R.B. "Degree of approximation of a function by Norlund means of its Fourier series", Bull. Austral. Math. Soc., 1981; 23(3): pp. 395-412. doi:10.1017/S0004972700007279

Siddiqi A.H. "On the degree of approximation to a function by Cesaro means of its Fourier series", Indian J. Pure Appl. Math., 1971; 2(3): pp. 367-373.


Bojtsun L.G. "On absolute summability of conjugate Fourier integrals by method of G.F. Voronoi", Izv. VUZov. Matem., 1967; 6: pp. 11-21.

Bojtsun L.G., Rybnikova T.I. "On degree of approximation of function by Cesaro means of its Fourier integral", Res. Math., 1974: pp. 8-16.

Bojtsun L.G., Rybnikova T.I. "On degree of approximation of function by Cesaro means of its Fourier integral", Res. Math., 1975: pp. 16-23.

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

Lipovik V.V. "On approximation in strong sense by truncated Fourier integral", Res. Math., 1972: pp. 50-53.

Lipovik V.V. "On estimates of strong approximation of functions by truncated Fourier integrals", Theory of approximation of functions. Proc. Int. Conf. on Approx. Theory, 1983; pp. 260-262.

Lipovik V.V., Khoroshko N.P. "On degree of strong approximation of functions by truncated Fourier integrals", Res. Math., 1979: pp. 13-16.

Natanson I.P. "On one method of Fourier integrals summation", Matem. sbor., 1940; 7(2): pp. 313-320.

Ponomarenko V.G. "Fourier integrals and the best approximation by entire functions", Doklady AN sssr, 1962; 147(3): pp. 556-558.

Ponomarenko V.G. "Research on modern problems of constructive function theory", 1965; pp. 85-88.

Ponomarenko V.G. "Fourier integrals and the best approximation by entire functions. On question of Fourier integral summation.", Izv. VUZov. Matem., 1976; 168(5): pp. 86-91.

Titchmarsh E.C. Introduction to the theory of Fourier integral, 1948.




DOI: https://doi.org/10.15421/241104

  

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Copyright (c) 2011 L.G. Bojtsun, T.I. Rybnikova

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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
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