Approximation of classes of Poisson integrals by rectangular Fejér means

Abstract

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The article is devoted to the problem of approximation of classes of periodic functions by rectangular linear means of Fourier series. Asymptotic equalities are found for upper bounds of deviations in the uniform metric of rectangular Fejér means on classes of periodic functions of several variables generated by sequences that tend to zero at the rate of geometric progression. In one-dimensional cases, these classes consist of Poisson integrals, namely functions that can be regularly extended in the fixed strip of a complex plane.

Keywords

• linear method of approximation
• extremal problem of approximation theory
• Poisson integral
• Fejér mean
• exact asymptotic