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...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.展开更多
The remainders and the convergence of cardinal polyharmonic spline interpolation are studied, and the asymptotic behavior of the best approximation by polyharmonic spline and the average K-width of some class of smoot...The remainders and the convergence of cardinal polyharmonic spline interpolation are studied, and the asymptotic behavior of the best approximation by polyharmonic spline and the average K-width of some class of smooth functions defined on the Euclidean space Rn are determined.展开更多
文摘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.
文摘The remainders and the convergence of cardinal polyharmonic spline interpolation are studied, and the asymptotic behavior of the best approximation by polyharmonic spline and the average K-width of some class of smooth functions defined on the Euclidean space Rn are determined.
