Potentiels isorésonants et symétries

Abstract : In this PhD thesis we consider the finite meromorphic continuation of the resolvent of the free Laplacian on complete manifolds with dimension n greater than 2. The poles of this continuation are called resonances. We assume that the manifold has some symmetries like S^1, (S^1)^m or SO(n). With this condition, we construct potentials V which are isoresonant i.e. such that the Laplacian plus V has the same resonances as the free Laplacian with the same multiplicities. During this construction we had to find an estimate of the first term of the spectrum of the Laplacian acting on S^1 homogeneous functions with compact support. We also show that these isoresonant potentials can change the order of the resonances. Finally, sometimes, resonances are defined as the poles of the scattering operator : we prove that in this framework we also have the isoresonance of our potentials.
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Submitted on : Wednesday, November 5, 2008 - 12:04:48 PM
Last modification on : Monday, March 25, 2019 - 4:52:05 PM
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Aymeric Autin. Potentiels isorésonants et symétries. Mathématiques [math]. Université de Nantes, 2008. Français. ⟨tel-00336843⟩

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