Uniform resolvent estimates for critical magnetic Schrödinger operators in 2D
Abstract
We study the $L^p-L^q$-type uniform resolvent estimates for 2D-Schrödinger 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.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2021
- DOI:
- 10.48550/arXiv.2109.11327
- arXiv:
- arXiv:2109.11327
- Bibcode:
- 2021arXiv210911327F
- Keywords:
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- Mathematics - Analysis of PDEs;
- Mathematics - Spectral Theory
- E-Print:
- 31 pages. We add some remarks after Theorem 1.2 and correct some typos in the new version. Comments are welcome!