On the optimization of direct methods for solving fredholm integral equations of the second kind with infinitely smooth kernels

We give a direct method, optimal inL ₂, for solving the Fredholm integral equation of the second kind with operators acting into the space of functions harmonic in a disk or into the space of functions that can be analytically extended to an infinite strip. The exact order of the error of this method is determined.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 12, pp. 1695–1701, December, 1993.