On approximation of continuous periodic functions by Stechkin's polynomials

O.V. Kotova

doi:10.15421/241314

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

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