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Applications of Resonance Theory Without Analyticity Assumption

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  • Additional Information
    • Contributors:
      Institut de Mathématiques de Bordeaux (IMB); Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS); Laboratoire de Mathématiques d'Orsay (LMO); Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)
    • Publication Information:
      Springer Science and Business Media LLC, 2021.
    • Publication Date:
      2021
    • 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.
      Comment: 49 pages, 12 figures
    • ISSN:
      1424-0661
      1424-0637
    • Accession Number:
      10.1007/s00023-021-01065-w
    • Accession Number:
      10.1007/s00023-021-01065-w⟩
    • Rights:
      OPEN
    • Accession Number:
      edsair.doi.dedup.....ca1d98e7c6bd1101f1124b6a4bc3c11b