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

Luca Fanelli; Junyong Zhang; Jiqiang Zheng

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

Analysis of PDEs 2021-09-27 v2 Spectral Theory

Authors: Luca Fanelli , Junyong Zhang , Jiqiang Zheng

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.

Keywords

uniform resolvent estimates schrödinger operators magnetic fields aharonov-bohm localization eigenvalue perturbations

Cite

@article{arxiv.2109.11327,
  title  = {Uniform resolvent estimates for critical magnetic Schr\"odinger operators in 2D},
  author = {Luca Fanelli and Junyong Zhang and Jiqiang Zheng},
  journal= {arXiv preprint arXiv:2109.11327},
  year   = {2021}
}

Comments

31 pages. We add some remarks after Theorem 1.2 and correct some typos in the new version. Comments are welcome!

Related papers

View all related →