Uniform approximations by Fourier sums on classes of convolutions of periodic functions

2020/01/02 by A. S. Serdyuk, Serdyuk, A. S., T. A. Stepanyuk +1
Mathematics · #Mathematical Approximation and Integration #Approximation Theory and Sequence Spaces

paper · pdf · doi:10.48550/arxiv.2001.00374

Abstract

We establish asymptotic estimates for exact upper bounds of uniform approximations by Fourier sums on the classes of 2π-periodic functions, which are represented by convolutions of functions φ(φ\bot 1) from unit ball of the space L₁ with fixed kernels Ψ_β of the form Ψ_β(t)=∑_k=1^∞ψ(k) cos(kt-(βπ)/(2)), ∑_k=1^∞kψ(k)

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