Modulation type spaces for generators of polynomially bounded groups and Schrödinger equations

We introduce modulation type spaces associated with the generators of polynomially bounded groups. Besides strongly continuous groups we study in detail the case of bi-continuous groups, e.g. weak-continuous groups in dual spaces. It turns out that this gives new insight in situations where generators are not densely defined. Classical modulation spaces are covered as a special case but the abstract formulation gives more exibility. We illustrate this with an application to a nonlinear Schrödinger equation. Mathematics Subject Classification (2010). 47D06, 47A60, 47D08, 35Q55.