Hilbert-space methods in elliptic partial differential equations

The purpose of this paper is to study, together with applications, those aspects of the theory of Hubert Space which are pertinent to the theory of elliptic partial differential equations. This involves the study of an unbounded operator A from one Hubert Space to another together with its adjoint A*, its pseudo-inverse or generalized reciprocal A" 1 , and its ^-reciprocal A 1 -A*~. In order to carry out the results, further properties of the operators A~ and A' are developed in this paper.