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Theses

Estimations dispersives

Abstract : There are four important results in my thesis.

For a large class of real-valued potentials, V(x), in dimension higher than 4 , we prove dispersive estimates for the low frequency part of the Schrödinger propagator, provided the zero is neither an eigenvalue nor a resonance. This class includes decreasing potentials satisfying V(x)=O(^{-(n+2)/2-\epsilon}). As a consequence, we extend the results in Journé, Soffer and Sogge to a larger class of potentials.

We prove dispersive estimates at low frequency in dimensions higher than 4 for the wave equation for a very large class of real-valued potentials, provided the zero is neither an eigenvalue nor a resonance. This class includes decreasing potentials satisfying V(x)=O(^{-(n+1)/2-\epsilon}).

We prove dispersive estimates at high frequency in dimension two for both the wave and the Schrödinger groups for a very large class of real-valued potentials.
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https://tel.archives-ouvertes.fr/tel-00196063
Contributor : Simon Moulin <>
Submitted on : Wednesday, December 12, 2007 - 10:25:11 AM
Last modification on : Monday, March 25, 2019 - 4:52:05 PM
Long-term archiving on: : Friday, November 25, 2016 - 7:42:38 PM

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  • HAL Id : tel-00196063, version 1

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Simon Moulin. Estimations dispersives. Mathématiques [math]. Université de Nantes, 2007. Français. ⟨tel-00196063⟩

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