Approximation methods for a class of discrete Wiener-Hopf equations

Abstract

In this paper, we consider approximation methods for operator equations of the form $Au + Bu = f$, where $A$ is a discrete Wiener-Hopf operator on $l_{p}$ $1 \leq p \lt \infty$ which symbol has roots on the unit circle with arbitrary multiplicities (not necessary integers). Conditions on perturbation $B$ and $f$ are given in order to guarantee the applicability of projection-iterative methods. Effective error estimates, and simultaneously, decaying properties for solutions are obtained in terms of some smooth spaces.