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Semi-groupes integres d'operateurs, l'unicite des pre-generateurs et applications

Abstract : Ours main purpose is the uniqueness problem for the diffusion operators on $L^\infty$. This work begin by a study of the $C_0$-semigroups and of the integrated semigroups in a very general context. We study the $C_0$-semigroups on a locally convex space and we introduce a new topology on the dual space such that the adjoint of a $C_0$-semigroup becomes a $C_0$-semigroup with repect of this topology. The most important results are a caracterization theorem of a core of a generator and a complet caracterization theorem of an essential generator on a locally convex space. Finaly, we presents several examples of essential generators on $L^\infty$. In this theses is obtained for the first time the $L^\infty$-uniqueness of Schroedinger operators and generalized Schroedinger operators on a complet riemannian manifold, and the $L^1$-uniqueness for the weak solutions of the mass transport equation.
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https://tel.archives-ouvertes.fr/tel-00139507
Contributor : Ludovic Dan Lemle <>
Submitted on : Saturday, March 31, 2007 - 8:06:37 PM
Last modification on : Thursday, January 11, 2018 - 6:20:33 AM
Long-term archiving on: : Friday, September 21, 2012 - 1:40:24 PM

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  • HAL Id : tel-00139507, version 1

Citation

Ludovic Dan Lemle. Semi-groupes integres d'operateurs, l'unicite des pre-generateurs et applications. Mathématiques [math]. Université Blaise Pascal - Clermont-Ferrand II, 2007. Français. ⟨tel-00139507⟩

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