Isoresonant complex-valued potentials and symmetries

Details Isoresonant complex-valued potentials and symmetries Isoresonant complex-valued potentials and symmetries

2009-05-08

arxiv.org/abs/0905.1277v1

Mathematics

Spectral Theory

32 pages

Scientific paper

Let $X$ be a connected Riemannian manifold such that the resolvent of the free Laplacian $(\Delta-z)^{-1}, z\in\C\setminus\R^{+},$ has a meromorphic continuation through $\R^{+}$. 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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