Convolution Operators With Spline Kernels - Osman, Rohaizan (1994)
In this project, we shall derive the asymptotic formulas for convolution operators with spline kernels for higher order differentiable functions. The two classes of operators which will be considered are the de la Vallee Poussin-Schoenberg operators Tm,k with trigonometric B-spline kernel of degree m and the singular integrals of Riemann-Lebesgue Rn,k with the periodic B-spline kernel of degree n -1. These formulas are analogous to the Bernstein's extension of Voronovskaya's estimate for Bernsteins polynomials and Marsden and Riemenschneider's extension of Bernstein-Schoenberg operators for higher order derivatives.