On the Cardinal Spline Interpolation Corresponding to Infinite Order Differential Operators

This paper discusses some problems on the cardinal spline interpolation correspond- ing to infinite order differential operators. The remainder formulas and a dual theorem are es- tablished for some convolution classes, where the kernels are PF densities. Moreover, the exact error of approximation of a convolution class with interpolation cardinal splines is determined. The exact values of average n-Kolmogorov widths are obtained for the convolution class.