Factorization of abstract operators into two second degree operators and its applications to integro-differential equations

Abstract

Boundary value problem B1x = f with an abstract linear operator B1, corresponding to an Fredholm integro-differential equation with ordinary or partial differential operator is researched. An exact solution to B1x = f in the case when a bijective operator B1 has a factorization of the form B1 =BB0 where B and B0 are two linear more simple than B1 second degree abstract operators, received. Conditions for factorization of the operator B1 and a criterion for bijectivity of B1 are found.