2003 Prépublication d'Orsay numéro 2003-47 (06/10/2003)



COMMUTATORS, C^0 GROUPS AND RESOLVENT ESTIMATES

GEORGESCU, V. - Analyse Numérique et E.D.P., Université de Cergy-pontoise, 95302 Cergy-Pontoise cédex
GERARD, C. - Analyse Numérique et E.D.P., Université Paris-Sud, Bât. 425, 91405 Orsay cedex
MOLLER, J.S. - Analyse Numérique et E.D.P., Universitat Mainz - Germany



Mots Clés : .

Classification MSC : 81T08#82B21#82B31#46L55



Resumé :

Abstract :
We study the existence and the continuity properties of the boundary values $(H-\lambda\pm\i0)^{-1}$ of the resolvent of a selfadjoint operator $H$ in the framework of the conjugate operator method initiated by E.\ Mourre. We allow the conjugate operator $A$ to be the generator of a $C_0$-semigroup (finer estimates require $A$ to be maximal symmetric) and we consider situations where the first commutator $[H,\i A]$ is not comparable to $H$. The applications include the spectral theory of zero mass quantum field models.

Contact : Christian.Gerard@math.u-psud.fr