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Commutators, C0-semigroups and resolvent estimates |
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| Authors: | V Georgescu C Gérard |
| Institution: | a Unite CNRS-UMR 8088 and Département de Mathématiques, Université de Cergy-Pontoise, FR-95302 Cergy-Pontoise Cédex, France b Département de Mathématiques, Université de Paris Sud, FR-91405 Orsay Cedex, France c FB Mathematik (17), Johannes Gutenberg Universität-Mainz, D-55099 Mainz, Germany |
| Abstract: | We study the existence and the continuity properties of the boundary values on the real axis of the resolvent of a self-adjoint operator H in the framework of the conjugate operator method initiated by Mourre. We allow the conjugate operator A to be the generator of a C0-semigroup (finer estimates require A to be maximal symmetric) and we consider situations where the first commutator H,iA] is not comparable to H. The applications include the spectral theory of zero mass quantum field models. |
| Keywords: | C0- semigroups Resolvent estimates Conjugate operator Positive commutators Mourre estimate Boundary values of resolvent families Virial theorem |
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