This paper is devoted to the study of the cut-off resolvent of a semiclassical "black box'' operator . We estimate the norm of , for any , by the norm of where and . For in the unphysical sheet with , we prove that this estimate holds with a constant . We also study the resonant states of the operator and we obtain bounds for by . These results hold without any assumption on the trapped set nor any assumption on the multiplicity of the resonances.
Cite this article
Jean-François Bony, Vesselin Petkov, Semiclassical estimates of the cut-off resolvent for trapping perturbations. J. Spectr. Theory 3 (2013), no. 3, pp. 399–422DOI 10.4171/JST/49