# Opérateurs de Schrödinger et transformée de Riesz sur les variétés complètes non-compactes

Abstract : In a first part, we give a necessary and sufficient condition so that a Schrödinger operator on a complete non-compact manifold has a finite number of negative eigenvalues. In a second part, we study the Riesz transform on a class of complete non-compact manifolds satisfying a Sobolev inequality. We first show a Gaussian estimate for the heat kernel of generalise Schrödinger operators, for example the Hodge Laplacian acting on differential forms, then we use this to show that the Riesz transform is bounded on the $L^p$ spaces for $p$ between $1$ and the Sobolev dimension. Finally, we show a perturbation result for the Riesz transform.
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Document type :
Theses
Mathématiques [math]. Université de Nantes, 2011. Français
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https://tel.archives-ouvertes.fr/tel-00631134
Contributor : Baptiste Devyver <>
Submitted on : Friday, September 12, 2014 - 5:11:42 PM
Last modification on : Friday, March 27, 2015 - 10:00:34 AM

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• HAL Id : tel-00631134, version 2

### Citation

Baptiste Devyver. Opérateurs de Schrödinger et transformée de Riesz sur les variétés complètes non-compactes. Mathématiques [math]. Université de Nantes, 2011. Français. <tel-00631134v2>

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