03-197 Vladimir Georgescu, Christian Gerard, Jacob Schach-Moeller

Commutators, $C_{0}-$ semigroups and Resolvent Estimates (695K, Postscript) Apr 27, 03

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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.

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