A new look at Mourre's commutator theory

Sylvain Golénia (1) , Thierry Jecko (2)

1 KMMF - Department of Mathematical Methods in Physics [Warsaw]
2 IRMAR - Institut de Recherche Mathématique de Rennes

Mourre's commutator theory is a powerful tool to study the continuous spectrum of self-adjoint operators and to develop scattering theory. We propose a new approach of its main result, namely the derivation of the limiting absorption principle (LAP) from a so called Mourre estimate. We provide a new interpretation of this result

Mots clés: Mourre's commutator theory; Mourre estimate; limiting absorption principle; continuous spectrum

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

Sylvain Golénia, Thierry Jecko. A new look at Mourre's commutator theory. Complex Analysis and Operator Theory, 2007, 1 (3), pp.399-422. ⟨10.1007/s11785-007-0011-4⟩. ⟨hal-00368976⟩