Bound states and scattered states for contraction semigroups


Let A generate a strongly continuous contraction semigroup {T(t)} on a Hilbert space and let L be a bounded operator. If L(ζI-A)-1 is compact, then the Cesàro limit of {norm of matrix}LT(t)f{norm of matrix}2 (as t→∞) is computed for all vectors f. This limit is interpreted in terms of bound and scattered states in the context of quantum mechanical and classical wave propagation problems. © 1985 D. Reidel Publishing Company.

Publication Title

Acta Applicandae Mathematicae