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Article Dans Une Revue Annales Henri Poincaré Année : 2021

Applications of resonance theory without analyticity assumption

Jean-François Bony
Thierry Ramond

Résumé

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 Schrödinger 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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Dates et versions

hal-02400101 , version 1 (22-11-2021)

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Jean-François Bony, Laurent Michel, Thierry Ramond. Applications of resonance theory without analyticity assumption. Annales Henri Poincaré, 2021, 22 (11), pp.3641-3697. ⟨10.1007/s00023-021-01065-w⟩. ⟨hal-02400101⟩
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