Finite-dimensioanl perturbations of linear operators and some applications to boundary integer equations

摘要

Finite-dimensioanl perturbing operators are constructed using some incomplete information about eighteen-solutions of an original and/or adjoin generalized Fredholm operator equation (with zero index). Adding such a perturbing operator to the original one reduces the eighenspace dimension and can, particularly, lead to an unconditionally and uniquely solvable perturbed equation. For the second ind Fredholm operators, the perturbing operators are analyzed such that the spectrum points for an original and the perturbed operators coincide except a spectrum point considered, which can be removed for the perturbed operator. A relation between resolvents of original and perturbed operators is obtained. Effective procedures are described for calculation of the undetermined constants in the right-hand side of an operator equation for the case when these constants must be chosen to satisfy the solvability conditions not written explicitly. Implementation of the methods is illustrated on a boundary integral equation of elasticity.