Semiclassical resolvent estimates for matrix Schrödinger operators and applications.

We establish semiclassical resolvent estimates for Schrödinger operators with long-range matrix-valued potentials. As an application, we prove a resonance-free domain in trapping situations. These results generalize the well-known results of [4] [N. Burq, Lower bounds for shape resonances widths of long range Schrödinger operators, <italic>Amer. J. Math.</italic> <bold>124</bold>(4) (2002) 677–735] in the case of scalar Schrödinger operators. In addition, we give an estimate on the scattering amplitude for Schrödinger operators with compactly supported matrix-valued potentials. [ABSTRACT FROM AUTHOR]