The finite-section approximation for integral equations on the half-line

Integral equations on the half line are commonly approximated by the finite-section approximation, in which the infinite upper limit is replaced by a positive number β. A novel technique is used here to rederive a number of classical results on the existence and uniqueness of the solution of the Wiener-Hopf and related equations, and is then extended to obtain existence, uniqueness and convergence results for the corresponding finite-section equations. Unlike the methods used in the recent work of Anselone and Sloan, the present methods are constructive, and result in explicit asymptotic bounds for the error introduced by the finite-section approximation.