Resolvent estimates and resonance free domains for Schrödinger operators with matrix-valued potentials

DOI10.1007/978-3-030-55556-6_2zbMATH Open1465.35130arXiv2009.03867OpenAlexW3084000719MaRDI QIDQ2662769

Marouane Assal

Publication date: 14 April 2021

Abstract: We establish semiclassical resolvent estimates for Schr"odinger 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 cite{Burq1, Martinez1} in the case of scalar Schr"odinger operators.

Full work available at URL: https://arxiv.org/abs/2009.03867

zbMATH Keywords

Carleman estimatesmatrix Schrödinger operatorssemiclassical resolvent estimatesresonance free domains

Mathematics Subject Classification ID

Spectrum, resolvent (47A10) Schrödinger operator, Schrödinger equation (35J10)

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