Fliess operators on Lp spaces: convergence and continuity

Fliess operators as input-output mappings are particularly useful in a number of fundamental problems concerning nonlinear realization theory. In the classical analysis of these operators, certain growth conditions on the coefficients in their series representations insure uniform and absolute convergence, provided each admissible input is uniformly bounded by some fixed upper bound. In some emerging applications of this theory, however, it is more natural to consider other classes of inputs. In this paper, L_p function spaces are considered. In particular, growth conditions are developed which provide sufficient conditions for convergence and continuity, and ensure that any realization of the operator yields a well defined state space model on the input space