Approximation by interpolation trigonometric polynomials on classes of periodic analytic functions

  • A. S. Serdyuk

Abstract

We establish asymptotically unimprovable interpolation analogs of Lebesgue-type inequalities on the sets $C^{\psi}_{\beta}L_p$ of $(\psi, \beta)$-differentiable functions generated by sequences $\psi(k)$ that satisfy the d'Alembert conditions. We find asymptotic equalities for the least upper bounds of approximations by interpolation trigonometric polynomials on the classes $C^{\psi}_{\beta, p},\;\; 1 \leq p \leq \infty$.
Published
25.05.2012
How to Cite
SerdyukA. S. “Approximation by Interpolation Trigonometric Polynomials on Classes of Periodic Analytic Functions”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, no. 5, May 2012, pp. 698-12, http://umj.imath.kiev.ua/index.php/umj/article/view/2609.
Section
Research articles