Uniform Resolvent Estimates for Critical Magnetic Schrödinger Operators in 2D

DOI10.1093/IMRN/RNAC362arXiv2109.11327OpenAlexW3200043621MaRDI QIDQ6182595

Ji Qiang Zheng, Jun Yong Zhang, Luca Fanelli

Publication date: 25 January 2024

Published in: Unnamed Author (Search for Journal in Brave)

Abstract: 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.

Full work available at URL: https://arxiv.org/abs/2109.11327

zbMATH Keywords

resolvent estimates magnetic Schrödinger operator

Mathematics Subject Classification ID

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

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