Resonances for nonanalytic potentials (Q847034)

The authors develop a resonance theory for Schröginger operators with a nonanalytic potential. They apply it to the nontrapping case (where no resonance appear in some energy region) and to the case of a ``point-well in an island'' (with shape resonances). Replacing the original potential by some suitable analytic approximations, the authors considers the usual resonances obtained by analytic distorsion. Roughly speaking, these resonances concentrate on some discrete set (which will be the set of resonance of the original operator) as the approximation becomes better and better. The author show that this set is independent of the choice of the analytic approximations (improving this way a previous result in [\textit{C. Cancelier, A. Martinez} and \textit{T. Ramond}, Asymptotic Anal. 44, No. 1-2, 47--74 (2005; Zbl 1095.35015)]. The theory is based on resolvent estimates which are uniform in some approximation parameter and are derived via precise arguments from a Grushin problem. We refer to the very clear Introduction for more details.