On vector-valued Schrödinger operators with unbounded diffusion in $$L^p$$ spaces

Abstract

AbstractWe prove generation results of analytic strongly continuous semigroups on $$L^p({{\mathbb {R}}}^d,{{\mathbb {R}}}^m)$$ L p ( R d , R m ) ($$1<p<\infty $$ 1 < p < ∞ ) for a class of vector-valued Schrödinger operators with unbounded coefficients. We also prove Gaussian type estimates for such semigroups.