SEMICLASSICAL RESOLVENT ESTIMATES FOR THE MAGNETIC SCHR ÖDINGER OPERATOR - Centre Henri Lebesgue
Pré-Publication, Document De Travail Année : 2025

SEMICLASSICAL RESOLVENT ESTIMATES FOR THE MAGNETIC SCHR ÖDINGER OPERATOR

Georgi Vodev
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Résumé

We obtain semiclassical resolvent estimates for the Schrödinger operator (ih∇ + b)^2 + V in R^d , d ≥ 3, where h is a semiclassical parameter, V and b are real-valued electric and magnetic potentials independent of h. Under quite general assumptions, we prove that the norm of the weighted resolvent is bounded by exp(Ch^{-2} log(h^{ -1} )) . We get better resolvent bounds for electric potentials which are Hölder with respect to the radial variable and magnetic potentials which are Hölder with respect to the space variable. For long-range electric potentials which are Lipschitz with respect to the radial variable and long-range magnetic potentials which are Lipschitz with respect to the space variable we obtain a resolvent bound of the form exp(Ch^{-1}) .
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Dates et versions

hal-04881572 , version 1 (12-01-2025)

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  • HAL Id : hal-04881572 , version 1

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Georgi Vodev. SEMICLASSICAL RESOLVENT ESTIMATES FOR THE MAGNETIC SCHR ÖDINGER OPERATOR. 2025. ⟨hal-04881572⟩
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