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Resolvent Estimates and Resonance Free Domains for Schrödinger Operators with Matrix-Valued Potentials

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Spectral Theory and Mathematical Physics

Part of the book series: Latin American Mathematics Series ((LAMSUFSC))

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Abstract

We establish semiclassical resolvent estimates for Schrödinger operators with long-range matrix-valued potentials. As an application we prove resonance free domains both in trapping and non-trapping situations. Our results generalize the well-known results of Burq (Am J Math 124(4):677–735, 2002), Martinez (Ann Henri Poincaré 4:736–75, 2002) in the case of scalar Schrödinger operators.

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Acknowledgements

The author is grateful to the organizers of the Conference “Spectral Theory and Mathematical Physics” at the Pontificia Universidad Católica de Chile for their kind invitation in December 2018. The author thank Gilles Lebeau for valuable discussions about Carleman estimates at Université de Nice in 2018. The author also thank Claudio Fernández for many stimulating remarks. The research of the author was supported by CONICYT FONDECYT Grant No. 3180390.

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Authors and Affiliations

  1. Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Santiago, Chile

    Marouane Assal

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  1. Marouane Assal
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Correspondence to Marouane Assal .

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Editors and Affiliations

  1. Departamento de Matemáticas y C. C., Universidad de Santiago de Chile, Santiago, Chile

    Pablo Miranda

  2. Institut de Mathématiques de Bordeaux, Talence, Gironde, France

    Nicolas Popoff

  3. Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Santiago, Chile

    Georgi Raikov

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Assal, M. (2020). Resolvent Estimates and Resonance Free Domains for Schrödinger Operators with Matrix-Valued Potentials. In: Miranda, P., Popoff, N., Raikov, G. (eds) Spectral Theory and Mathematical Physics. Latin American Mathematics Series(). Springer, Cham. https://doi.org/10.1007/978-3-030-55556-6_2

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