Abstract
On the classes of periodic functions C ψβ H β, we study approximating properties of trigonometric polynomials generated by methods for summation of Fourier series.
References
A. I. Stepanets, Classes of Periodic Functions and Approximation of Their Elements by Fourier Sums [in Russian], Preprint No. 83.10, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1983).
A. I. Stepanets, “Classification of periodic functions and the rate of convergence of their Fourier series,” Izv. Akad. Nauk SSSR, Ser. Mat., 50, No. 1, 101–136 (1986).
A. I. Stepanets, The Rate of Convergence of Fourier series in Spaces L ψβ [in Russian], Preprint No. 86.66, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1986).
A. I. Stepanets, Classification and Approximation of Periodic Functions [in Russian], Naukova Dumka, Kiev (1987).
A. I. Stepanets, Approximation by Entire Functions in a Uniform Metric [in Russian], Preprint No. 88.27, Institute of Mathematics Ukrainian Academy of Sciences, Kiev (1988).
A. I. Stepanets, “Approximation by Fourier operators of functions defined on the real axis,” Ukr. Mat. Zh., 40, No. 2 198–209 (1988).
A. I. Stepanets, “Classes of functions defined on the real axis and their approximations by entire functions. I,” Ukr. Mat. Zh., 42, No. 1, 102–112 (1990).
A. I. Stepanets, “Classes of functions defined on the real axis and their approximations by entire functions. II, Ukr. Mat. Zh., 42, No. 2, 210–222, (1990).
A. I. Stepanets, “Approximation in spaces of locally integrable functions,” Ukr. Mat. Zh., 46, No. 5, 597–625 (1994).
V. I. Rukasov, Approximation of Periodic Functions by the Linear Averages of Their Fourier Series [in Russian], Preprint No. 83.62, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1983).
Yu. I. Kharkevich, On Approximation of Functions of the Classes C ψβ Hω by the Linear Averages of their Fourier Series [in Russian], Preprint No. 91.8. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1991).
V. I. Rukasov, “Approximation of functions defined on the real axis by the de la Vallée-Poussin operators,” Ukr. Mat. Zh., 44, No. 5, 682–690 (1992).
O. A. Novikov and V. I. Rukasov, “Approximation of classes of continuous periodic functions by analogs of the de la Vallée-Poussin sums,” in: Fourier Series. Theory and Application (Collection of Scientific Works) [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1992), pp. 57–63.
C. M. Nikol’skii, “Approximation of periodic functions by trigonometric polynomials,” in: Tr. Mat. Inst. Akad Nauk USSR, 15, 1–76 (1945).
S. M. Nikol’skii, “A Fourier series of functions with a given modulus of continuity,” Dokl. Akad Nauk SSR, 52, 191–193 (1945).
A. V. Efimov, “Linear methods of approximation of certain classes of continuous periodic functions,” in: Tr. Mat. Inst. Akad Nauk USSR, 62, 3–47 (1961).
A. V. Efimov, “On the approximation of periodic functions by the de la Vallée-Poussin sums. I,” Izv. Akad Nauk USSR. Ser. Mat., 23, No. 5, 737–770 (1959).
A. I. Efimov, “On approximation of periodic functions by the de la Vallée-Poussin sums. II,” Izv. Akad Nauk USSR. Ser. Mat., 24, No.3, 431–468 (1959).
A. I. Gavrilyuk and A. I. Stepanets, “Approximation of differentiable functions by Rogozinskii polynomials,” Ukr. Mat. Zh., 25, No. 1, 3–134 (1973).
A. I. Stepanets, Uniform Approximations by Trigonometric Polynomials [in Russian], Naukova Dumka, Kiev (1981).
Additional information
Slavyansk Pedagogical Institute, Slavyansk. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 4, pp. 606–610, April, 1997.
Rights and permissions
About this article
Cite this article
Rukasov, V.I., Novikov, O.A. Approximation of the classes C ψβ H ω by generalized de la Valiée-Poussin sums. Ukr Math J 49, 672–677 (1997). https://doi.org/10.1007/BF02487332
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02487332