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 nonselfadjoint Schrödinger operators which are perturbation of a model operator satisfying some weighted coercive assumption. For the model operator, we prove that the derivatives of the resolvent satisfy some Gevrey estimates at the threshold zero. As application, we establish large time expansions for the semigroups e −tH and e −itH for t > 0 with subexponential time-decay estimates on the remainder. We also study the case when zero is an embedded eigenvalue of non-selfadjoint Schrödinger operators.

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

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-01508723v1⟩