Abstract
Asymptotic equalities are found for the least upper bounds of the best approximations of some convolution classes with even kernel in the metric of a spaceL p.
Similar content being viewed by others
References
N. P. Korneichuk,Extremal Problems of the Approximation Theory [in Russian], Nauka, Moscow (1976).
A. I. Stepanets,Classes of Periodic Functions and Approximation of Their Elements by the Fourier Sums [in Russian], Preprint Institute of Mathematics Ukrain. Acad. of Sciences, No. 10, Kiev (1983).
S. M. Nikolsky, “Approximation of functions by trigonometric polynomials in mean,”Izv. Akad. Nauk SSSR, Ser.Mat.,10, No. 3, 207–256 (1946).
S. B. Stechkin and S. A. Telyakowsky, “On approximating differentiable functions by trigonometric polynomials in the metricL,”Trudy Mat. Inst. Akad Nauk SSSR,88, 20–29 (1967).
P. V. Zaderei, “On approximation of periodic multivariable functions by trigonometric polynomials in the mean,” in:Methods of Approximation Theory and Their Applications [in Russian], Institute of Mathematics Ukrain. Acad. of Sciences, Kiev (1982), pp. 43–48.
V. P. Motorny, “Approximation of periodic functions by trigonometric polynomials in the mean,”Mat. zametki,16, No. 1, 15–26 (1974).
A. I. Stepanets and A. K. Kushpel',The Best Approximations and Widths of Classes of Periodic Functions [in Russian], Preprint Institute of Mathematics Ukrain. Acad. of Sciences, No. 15, Kiev (1984).
R. Edwards,Fourier Series in Modern Exposition [Russian translation], Vol. 2, Mir, Moscow (1985).
V. M. Tikhomirov,Some Problems in the Theory of Approximations [in Russian], Moscow State University, Moscow (1976).
A. Zygmund,Trigonometric Series [Russian translation], Vol. 1, Mir, Moscow (1965).
I. P. Natanson,Theory of Functions of Real Variable [in Russian], Nauka, Moscow (1974).
A. I. Stepanets,Classifying and Approximating Periodic Functions [in Russian], Naukova Dumka, Kiev (1987).
N. S. Gradshtein and I. M. Ryzhik,Tables of Integrals, Sums, Products, and Series [in Russian], Fizmatgiz, Moscow (1963).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 1, pp. 26–31, January, 1993.
Rights and permissions
About this article
Cite this article
Bushev, D.N., Koval'chuk, I.R. On approximation of convolution classes. Ukr Math J 45, 26–32 (1993). https://doi.org/10.1007/BF01062034
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01062034