Properties of the fundamental splines of the high order

In this paper, the properties of the fundamental splines of high orders are numerically studied. From the point of view of the interpolation problem, the fundamental spline is a nodal function generated by a family of integer translations of the corresponding basic spline. We have established that with increasing order fundamental splines tend to the sampling function sinc(πx). Analogous assertions were obtained earlier for nodal functions on the basis of other systems of shifts. The behavior of the coefficients of basic splines is studied. With the help of calculations, it is shown that for n>2 there is a sign-reversal and a monotone decreasing modulo.