On boundary functionals and operators with finite-dimensional null spaces
Franklin T. Iha · Pacific Journal of Mathematics · 1975
Let L be a closed operator on a Hubert space 3ίf defined on a linear manifold 2 of 'M with the property that L has a continuous right inverse T and that the dimension of the null space of L is finite.A boundary functional 17 for L is defined to be a linear functional η on 3) such that ηT is continuous.The boundary-value problems for ordinary differential equations are generalized to the operator L with the boundary conditions defined by a set of boundary functionals.It is shown, in particular, that if K is a continuous right inverse of L, then there exist n linearly independent boundary functionals, 171, , η n , where n is the dimension of the null space of L, such that the range of K is precisely the linear manifold {ueS)\η j (u) = 0J = 1,2, •• ,n}.