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Isoresonant Complex-valued Potentials and Symmetries

Published online by Cambridge University Press:  20 November 2018

Aymeric Autin
Aymeric Autin*
Affiliation:
11 rue Hélène Boucher, 85400 Luçon, France email: aymeric.autin@gmail.com
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Abstract

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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.

Keywords

31C1258J50
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 63 , Issue 4 , 01 August 2011 , pp. 721 - 754
Copyright
Copyright © Canadian Mathematical Society 2011

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