Limit theorems of the theory of discrete periodic splines

Abstract

It is known from the discrete harmonic analysis that the interpolation problem with equidistant interpolation points has a unique solution. If the right-hand sides in the interpolation problem are fixed, the spline depends on two parameters: the spline order and the number of points located between neighboring interpolation points. We find explicit expressions for the limits of interpolation spllines with respect to each parameter separately and show that both repeated limits exist. We also prove that these repeated limits are equal and their value is an interpolation trigonometric polynomial. Bibliography: 10 titles. Illustrations: 2 figures.