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Quantitative Limiting Absorption Principle in the Semiclassical Limit

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Abstract

We give an elementary proof of Burq’s resolvent bounds for long range semiclassical Schrödinger operators. Globally, the resolvent norm grows exponentially in the inverse semiclassical parameter, and near infinity it grows linearly. We also weaken the regularity assumptions on the potential.

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  1. Department of Mathematics, MIT, Cambridge, MA, 02139, USA

    Kiril Datchev

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  1. Kiril Datchev
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Correspondence to Kiril Datchev.

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Datchev, K. Quantitative Limiting Absorption Principle in the Semiclassical Limit. Geom. Funct. Anal. 24, 740–747 (2014). https://doi.org/10.1007/s00039-014-0273-8

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  • DOI: https://doi.org/10.1007/s00039-014-0273-8

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