Ergodic theory and iterative solution of linear operator equations

Abstract

In this paper we consider the problem of approximating solutions of linear operator equations of the type u-Tu=f. The main tools are Dotson's extension of the Eberlein ergodic theorem to affine mappings and the DeMoivre-Laplace theorem of probability theory. The main results are applied to obtain theorems on the iterative approximation of solutions of linear operator equations in Hilbert space and the approximation in L ^ρ norm of solutions of a certain functional equation in the space L ^∞