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Etude du pseudo-spectre d'opérateurs non auto-adjoints

Abstract : We study in this thesis the pseudospectrum of a class of non selfadjoint operators. More precisely, our work consists in the detailed study of microlocal properties, which rule the spectral stability or instability phenomena appearing under small perturbations for differential operators defined in Weyl quantization by complex valued elliptic quadratic symbols. We establish in this thesis a simple necessary and sufficient condition on the Weyl symbol of such operators, which ensures the stability of theirs spectra. When this condition is violated, we prove that it occurs some strong spectral instabilities for the high energies of these operators in some regions -- which can be far away from theirs spectra -- we give a precise geometrical description. To underline such spectral instabilities, we need to study and to establish some geometrical conditions, which ensure the existence of semiclassical quasimodes for general pseudodifferential operators.
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Contributor : Karel Pravda-Starov <>
Submitted on : Wednesday, October 25, 2006 - 7:58:18 PM
Last modification on : Friday, July 10, 2020 - 4:04:57 PM
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  • HAL Id : tel-00109895, version 1


Karel Pravda-Starov. Etude du pseudo-spectre d'opérateurs non auto-adjoints. Mathématiques [math]. Université Rennes 1, 2006. Français. ⟨tel-00109895⟩



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