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arXiv · 1912.02091

Applications of resonance theory without analyticity assumption

Jean-Francois Bony·Laurent Michel·Thierry Ramond
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Abstract

We prove that the results in scattering theory that involve resonances are still valid for non-analytic potentials, even if the notion of resonance is not defined in this setting. More precisely, we show that if the potential of a semiclassical Schr\"odinger operator is supposed to be smooth and to decrease at infinity, the usual formulas relating scattering quantities and resonances still hold. The main ingredient for the proofs is a resolvent estimate of a new type, relating the resolvent of an operator with the resolvent of its cut-off counterpart.

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Jean-Francois Bony, Laurent Michel, Thierry Ramond. 2019-12-04. Applications of resonance theory without analyticity assumption. https://arxiv.org/abs/1912.02091

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