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


Bojtsun L.G. "On absolute summability of conjugate Fourier integrals by method of G.F. 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, 1974: pp. 8-16. (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: 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)

Lipovik V.V. "On approximation in strong sense by truncated Fourier integral", Researches on modern problems of summation and approximation of functions and their applications, DGU, 1972: pp. 50-53. (in Russian)

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, Kyiv, 1983; pp. 260-262. (in Russian)

Lipovik V.V., Khoroshko N.P. "On degree of strong approximation of functions by truncated Fourier integrals", Researches on modern problems of summation and approximation of functions and their applications, DGU, 1979: pp. 13-16. (in Russian)

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

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

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

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

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

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.




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

  

Refbacks

  • There are currently no refbacks.


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

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


Registered in

More►


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