C₀-groups with Polynomial Growth

Abstract

We consider some conditions guaranteeing that an unbounded operator is a generator of some strongly continuous group satisfying a polynomial growth condition. The result is applied to a Friedrichs model given by T f (x) = xf(x)+ < f, φ > ψ (x) and considered as an operator in L^p (R). Some sufficient condition on φ and ψ are found such that iT generates an example of a group with polynomial growth.