GENERALIZED RESOLVENTS OF OPERATORS GENERATED BY INTEGRAL EQUATIONS

Abstract

We define a minimal operator L0 generated by an integral equation with an operator measure and give a description of the adjoint operator L∗0. We prove that every generalized resolvent of L0 is an integral operator and give a description of boundary value problems associated to generalized resolvents.

Keywords

• integral equation
• Hilbert space
• symmetric operator
• generalized resolvent
• boundary value problem