ON INTERPOLATION BY ALMOST TRIGONOMETRIC SPLINES

Abstract

The existence and uniqueness of an interpolating periodic spline defined on an equidistant mesh by the linear differential operator \({\cal L}_{2n+2}(D)=D^{2}(D^{2}+1^{2})(D^{2}+2^{2})\cdots (D^{2}+n^{2})\) with \(n\in\mathbb{N}\) are reproved under the final restriction on the step of the mesh. Under the same restriction, sharp estimates of the error of approximation by such interpolating periodic splines are obtained.

Keywords

• Splines, Interpolation, Approximation, Linear differential operator.