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Semiclassical resolvent estimates for Schrödinger matrix operators with eigenvalues crossing

Abstract : For semiclassical Schrödinger 2 × 2-matrix operators, the symbol of which has crossing eigenvalues, we investigate the semiclassical Mourre theory to derive bounds O(h −1) (h being the semiclassical parameter) for the boundary values of the resolvent, viewed as bounded operator on weighted spaces. Under the non-trapping condition on the eigenvalues of the symbol and under a condition on its matricial structure, we obtain the desired bounds for codimension one crossings. For codimension two crossings, we show that a geometrical condition at the crossing must hold to get the existence of a global escape function, required by the usual semiclassical Mourre theory.
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https://hal-cnrs.archives-ouvertes.fr/hal-03217327
Contributor : Thierry Jecko <>
Submitted on : Tuesday, May 4, 2021 - 5:40:25 PM
Last modification on : Thursday, May 6, 2021 - 3:35:34 AM
Long-term archiving on: : Thursday, August 5, 2021 - 8:04:33 PM

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Thierry Jecko. Semiclassical resolvent estimates for Schrödinger matrix operators with eigenvalues crossing. Mathematical News / Mathematische Nachrichten, Wiley-VCH Verlag, 2003, ⟨10.1002/mana.200310076⟩. ⟨hal-03217327⟩

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