2017
Том 69
№ 5

# Approximation by interpolation trigonometric polynomials on classes of periodic analytic functions

Serdyuk A. S.

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 $C^{\psi}_{\beta, p},\;\; 1 \leq p \leq \infty$.

English version (Springer): Ukrainian Mathematical Journal 64 (2012), no. 5, pp 797-815.

Citation Example: Serdyuk A. S. Approximation by interpolation trigonometric polynomials on classes of periodic analytic functions // Ukr. Mat. Zh. - 2012. - 64, № 5. - pp. 698-712.

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