Vladimir Georgescu, Christian Gerard, Jacob Schach-Moeller
Commutators, $C_{0}-$ semigroups and Resolvent Estimates
(695K, Postscript)
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.