English

Uniform approximations by Fourier sums on classes of generalized Poisson integrals

Classical Analysis and ODEs 2016-03-08 v1

Abstract

We find asymptotic equalities for exact upper bounds of approximations by Fourier sums in uniform metric on classes of 2π2\pi-periodic functions, representable in the form of convolutions of functions φ\varphi, which belong to unit balls of spaces LpL_{p}, with generalized Poisson kernels. For obtained asymptotic equalities we introduce the estimates of remainder, which are expressed in the explicit form via the parameters of the problem.

Keywords

Cite

@article{arxiv.1603.01891,
  title  = {Uniform approximations by Fourier sums on classes of generalized Poisson integrals},
  author = {A. S. Serdyuk and T. A. Stepaniuk},
  journal= {arXiv preprint arXiv:1603.01891},
  year   = {2016}
}

Comments

31 pages