Blog
About

  • Record: found
  • Abstract: found
  • Article: found
Is Open Access

Estimates of best \(m\)-term trigonometric approximation of classes of analytic functions

Preprint

Read this article at

Bookmark
      There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

      Abstract

      In metric of spaces \(L_{s}, \ 1\leq s\leq\infty\), we obtain exact in order estimates of best \(m\)-term trigonometric approximations of classes of convolutions of periodic functions, that belong to unit all of space \(L_{p}, \ 1\leq p\leq\infty\), with generated kernel \(\Psi_{\beta}(t)=\sum\limits_{k=1}^{\infty}\psi(k)\cos(kt-\frac{\beta\pi}{2})\), \(\beta\in \mathbb{R}\), whose coefficients \(\psi(k)\) tend to zero not slower than geometric progression. Obtained estimates coincide in order with approximation by Fourier sums of the given classes of functions in \(L_{s}\)-metric. This fact allows to write down exact order estimates of best orthogonal trigonometric approximation and trigonometric widths of given classes.

      Related collections

      Author and article information

      Journal
      2014-10-14
      1410.3866

      http://arxiv.org/licenses/nonexclusive-distrib/1.0/

      Custom metadata
      Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2015, No. 2, 32-37 (2015)
      7 pages, in Ukrainian
      math.CA

      Comments

      Comment on this article