Discrete Approximations for Multidimensional Singular Integral Operators

摘要

For discrete operator generated by singular kernel of Calderon-Zygmund one introduces a finite dimensional approximation which is a cyclic convolution. Using properties of a discrete Fourier transform and a finite discrete Fourier transform we prove a solvability for approximating equation in corresponding discrete space. For comparison discrete and finite discrete solution we obtain an estimate for a speed of convergence for a certain right-hand side of considered equation.