Izvestiya of Saratov University.
ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


Everywhere divergence of Lagrange processes on the unit circle

We study the convergence of Lagrange interpolation processes in the closed unit disk. Choosing a matrix with a certain distribution of interpolation nodes allowed to construct the set, completely covering the unit circle, and the function for which the process diverges everywhere on this set.

The Problem of Convergence in Point Trigonometric Interpolation Process of Lagrange

An analogue of the characteristic of R. Salem is obtained for a trigonometric Lagrange interpolation process on the matrix of equally spaced nodes.