HIGH FREQUENCY RESOLVENT ESTIMATES FOR THE MAGNETIC LAPLACIAN ON NON COMPACT MANIFOLDS - Institut de Mathématiques de Toulouse Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2024

HIGH FREQUENCY RESOLVENT ESTIMATES FOR THE MAGNETIC LAPLACIAN ON NON COMPACT MANIFOLDS

Résumé

We consider the Schrödinger operator with a magnetic perturbation on non compact manifolds with infinite volume. We prove optimal estimates for the resolvent operator at high frequencies in Besov-type spaces. In the general trapping case we obtain the usual exponential blow-up, while when the resolvent is localised on the manifold end, away from possible trapped trajectories, we obtain the optimal bound by the inverse square root of the spectral parameter.
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Dates et versions

hal-04513013 , version 1 (20-03-2024)

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  • HAL Id : hal-04513013 , version 1

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Viviana Grasselli. HIGH FREQUENCY RESOLVENT ESTIMATES FOR THE MAGNETIC LAPLACIAN ON NON COMPACT MANIFOLDS. 2024. ⟨hal-04513013⟩
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