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arxiv 2109.11327 v2 pith:6GXT3V3W submitted 2021-09-23 math.AP math.SP

Uniform resolvent estimates for critical magnetic Schr\"odinger operators in 2D

classification math.AP math.SP
keywords estimatesmagneticodingeroperatorsresolventuniformaharonov-bohmapplication
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We study the $L^p-L^q$-type uniform resolvent estimates for 2D-Schr\"odinger operators in scaling-critical magnetic fields, involving the Aharonov-Bohm model as a main example. As an application, we prove localization estimates for the eigenvalue of some non self-adjoint zero-order perturbations of the magnetic Hamiltonian.

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