A method of adjoints for solving some Ill-posed equations of the first kind

摘要

We consider solving the operator (1) where f may be badly behaved. It is shown that if one needs only linear functionals of the solution u, this may be accomplished by solving a related adjoint problem. This problem may be better posed than (1). Applications are made to several integral equations of the first kind, and it is shown that several apparently distinct procedures are particular cases of our result.