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Isoresonant Complex-valued Potentials and Symmetries
Published online by Cambridge University Press: 20 November 2018
Abstract
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.
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- Copyright © Canadian Mathematical Society 2011
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