Time-decay of semigroups generated by dissipative Schrödinger operators

Xue Ping Wang (1)

1 Equations aux dérivées partielles

We establish a representation formula for semigroups of contractions in terms of a global limiting absorption principle. As applications, we prove long-time asymptotics of the semigroup generated by $-iH$ where $ H $ is a dissipative Schrödinger operator.

Mots clés: Time-decay; dispersive estimate; semigroup of contractions; non-selfadjoint Schrödinger operators

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

Xue Ping Wang. Time-decay of semigroups generated by dissipative Schrödinger operators. Journal of Differential Equations, 2012, 253 (12), pp.3523-3542. ⟨hal-01005809⟩