L^p-theory for Schrödinger systems

In this article we study for p in (1,∞) the L^p-realization of the vector-valued Schroedinger operator Lu:= div(Q∇u) +V u. Using a noncommutative version of the Dore–Venni theorem due to Monniaux and Pruess, we prove that the L^p-realization of L, defined on the intersection of the natural domains of the differential and multiplication operators which form L, generates a strongly continuous contraction semigroup on L^p(R^d;C^m). We also study additional properties of the semigroup such as extension to L^1, positivity, ultracontractivity and prove that the generator has compact resolvent.