Resolvent Estimates and Resonance Free Domains for Schrödinger Operators with Matrix-Valued Potentials

We establish semiclassical resolvent estimates for Schrodinger operators with long-range matrix-valued potentials. As an application we prove resonance free domains both in trapping and non-trapping situations. Our results generalize the well-known results of Burq (Am J Math 124(4):677–735, 2002), Martinez (Ann Henri Poincare 4:736–75, 2002) in the case of scalar Schrodinger operators.