Approximation by interpolation trigonometric polynomials in metrics of the spaces $L_p$ on the classes of periodic entire functions

  • A. S. Serdyuk
  • I. V. Sokolenko

Abstract

We obtain the asymptotic equalities for the least upper bounds of approximations by interpolation trigonometric polynomials with equidistant distribution of interpolation nodes $x_{(n 1)}^k = \frac{2k\pi}{2n 1}, k \in Z,$, in metrics of the spaces $L_p$ on the classes of $2\pi$ -periodic functions that can be represented in the form of convolutions of functions $\varphi , \varphi \bot 1$, from the unit ball of the space $L_1$, with fixed generating kernels in the case where the modules of their Fourier coefficients $\psi (k)$ satisfy the condition $\mathrm{lim}_{k\rightarrow \infty} \psi (k + 1)/\psi (k) = 0.$. Similar estimates are also obtained on the classes of $r$-differentiable functions $W^r_1$ for the rapidly increasing exponents of smoothness $r (r/n \rightarrow \infty , n \rightarrow \infty )$.
Published
25.02.2019
How to Cite
SerdyukA. S., and SokolenkoI. V. “Approximation by Interpolation Trigonometric polynomials in Metrics of the Spaces $L_p$ on the Classes of Periodic Entire Functions”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, no. 2, Feb. 2019, pp. 283-92, http://umj.imath.kiev.ua/index.php/umj/article/view/1438.
Section
Research articles