Gevrey estimates of the resolvent and sub-exponential time-decay of solutions

Xue Ping Wang (1)

1 Equations aux dérivées partielles

In this article, we study a class of non-selfadjoint Schrödinger operators H which are perturbation of some model operator H 0 satisfying a weighted coercive assumption. For the model operator H 0 , we prove that the derivatives of the resolvent satisfy some Gevrey estimates at threshold zero. As application, we establish large time expansions of semigroups e −tH and e −itH for t > 0 with subexponential time-decay estimates on the remainder, including possible presence of zero eigenvalue and real resonances.

Mots clés: non-selfadjoint operators; Gevrey estimates; threshold spectral analysis; real resonances

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Théorie spectrale [math.SP]

Xue Ping Wang. Gevrey estimates of the resolvent and sub-exponential time-decay of solutions. 2017. ⟨hal-01508723v2⟩