Finite eigenfunction approximations for continuous spectrum operators (Q1204376)

The author introduces a new formulation of the theory of continuous spectrum eigenfunction expansions for self-adjoint operators in Hilbert space and analyzes the question of when operators are limits in an operator norm of finite sums of multiple of eigenprojections of multiplicity one. The theory, which unifies the treatment of continuous and discrete spectrum eigenfunction expansions, is applied to the study of ordinary and partial differential equations.