A partial inner product space of analytic functions for resonances

Generalized Hilbert spaces D (α,β) are defined using analytic continuation of Hardy class functions into a wedge bounded by the angles α,β. Eigenfunctions of isolated complex eigenvalues may be found in D (α,β) for operators that have a self-adjoint representation in L². These eigenvalues correspond to resonances in the associated decay problem. A bilinear form between D (α,β) and D (-β,-α) is defined, which has some of the properties of a Hilbert space scalar product, and it is shown that this form can be used to define a variational principle to obtain the eigenvalue equations.