On approximation of continuous periodic functions by Stechkin's polynomials

O.V. Kotova (Donetsk National University)


The answer to the V.I. Ivanov's question about the exact order approximation by Stechkin’s polynomials where s = 3 and s = 4 is obtained (s is the order of the modulus of smoothness). We use the method of Fourier multipliers and special differencing operators. The case where s = 2 was studied previously.


modulus of smoothness; K-functional; spline; Fourier-Budan’s theorem; Fourier multiplier; Fourier transform of measure; Beurling’s theorem


Draganov B.R. "Exact estimates of the rate of approximation of convolution operators", Journal Appr. Theory, 2010; 162: pp. 952-979.

Ivanov V.I. "Direct and inverse theorems of approximation theory for periodic functions in the works of S.B. Stechkin and their extension", Trudy IMM UroRAN, 2010; 16(4): pp. 5-17. (in Russian)

Kolomojtsev Yu.S., Trigub R.M. "On one non-classical method of approximation of periodic functions by trigonometrical polynomials", Ukr. matem. visnyk, 2012; 9(3): pp. 356-374. (in Russian)

Kotova O.V., Trigub R.M. "Exact order of approximation of periodic functions with one non-classical method of Fourier series summation", Ukrainian Math. J., 2012; 64(7): pp. 954-969. (in Russian)

Liflyand E., Samko S., Trigub R. "The Wiener Algebra of Absolutely Convergent Fourier Integrals: an overview", Analysis and Math.Physics, Springer, 2012; 2(1): pp. 1-68.

Prasolov V.V. Polynomials, MTSNMO, Moscow, 2001; 336 p. (in Russian)

Stein I., Weiss G. Introduction to Fourier analysis on Euclidean spaces, Mir, Moscow, 1974; 336 p. (in Russian)

Stechkin S.B. "On the order of the best approximation of continuous functions", Izv. AN SSSR, 1951; 15(3): pp. 219-242. (in Russian)

Trigub R.M. "Exact order of approximation of periodic functions by linear polynomial operators", East J. Approx., 2009; 15(1): pp. 25-50.

Trigub R.M., Belinsky E.S. Fourier Analysis and Approximation of functions, Kluwer-Springer, 2004; 585 p.

DOI: https://dx.doi.org/10.15421/241314



  • There are currently no refbacks.

Copyright (c) 2013 O.V. Kotova

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

Registered in

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