Isoresonant Complex-valued Potentials and Symmetries

Autin, Aymeric

Canadian journal of mathematics, Tome 63 (2011) no. 4, pp. 721-754

Résumé

Let $X$ be a connected Riemannian manifold such that the resolvent of the free Laplacian ${{(\Delta -z)}^{-1}},\,z\,\in \,\mathbb{C}\backslash {{\mathbb{R}}^{+}}$ , has a meromorphic continuation through ${{\mathbb{R}}^{+}}$ . The poles of this continuation are called resonances. When $X$ has some symmetries, we construct complex-valued potentials, $V$ , such that the resolvent of $\Delta \,+\,V$ , which has also a meromorphic continuation, has the same resonances with multiplicities as the free Laplacian.

Détail

DOI : 10.4153/CJM-2011-031-8

Mots-clés : 31C12, 58J50

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