Unbounded Operators on Hilbert Space

The theory developed thus far concentrated on bounded linear operators on a Hilbert space which had applications to integral equations. However, differential equations give rise to an important class of unbounded linear operators which are not defined on all of L2([a, b]). In this chapter an introduction to unbounded operators is presented which includes the spectral theorem for the Sturm-Liouville operator. Simple examples of the spectral theory of unbounded self adjoint operators are also given. For a more detailed theory the reader is referred to [G], [GGK1], [K] and [DS2].