On approximation of continuous periodic functions by Stechkin's polynomials

O.V. Kotova (Donetsk National University)

Abstract


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.

Keywords


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

References


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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)

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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)

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

  

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