Asymptotic error bounds in Galerkin approximation for a certain class of quasipotential equations

Error bounds for the Galerkin approximation of solutions to the eigenvalue problem are derived for a class of quasipotential integral equations. In the case of completely continuous operators conditions are derived under which the error in the approximate solutions of a spectral problem can be expanded in powers of a parameter $r^{-1}$, where $r$ is the length of the discretization interval of the integral operator, which is defined on a half-line.