This article is cited in 12 papers

On operators of interpolation with respect to solutions of a Cauchy problem and Lagrange–Jacobi polynomials

A. Yu. Trynin

Saratov State University named after N. G. Chernyshevsky

Abstract: We describe classes of continuous functions for which one has pointwise and uniform convergence of certain Lagrange-type operators (constructed from solutions of a Cauchy problem) and the Lagrange–Jacobi interpolation polynomials ${\mathcal L}_n^{(\alpha_{n},\beta_{n})}(F,\cos\theta)$. We also obtain sufficient conditions for the equiconvergence of these interpolation processes.

Keywords: interpolation processes, Lagrange operators, sampling theorem, theory of approximation of functions.

UDC: 517.518.85

MSC: 41A05, 41A35, 34B24

Received: 14.12.2009
Revised: 21.11.2010

DOI: 10.4213/im4275

 English version: Izvestiya: Mathematics, 2011, 75:6, 1215–1248

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