Uniform resolvent estimates for critical magnetic Schrödinger operators in 2D

2021/09/23 by Fanelli, Luca, Zhang, Junyong, Zheng, Jiqiang · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2109.11327

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.

Cited by

• Negative Order Bochner-Riesz Operators for the Critical Magnetic Schrödinger Operator in ℝ²

Related

• Uniform resolvent estimates for magnetic operators
• L^p resolvent estimates for magnetic Schrödinger operators with unbounded background fields
• Resolvent estimates for the magnetic Schrodinger operator
• Dispersive estimates of fourth order Schrödinger operators with scaling-critical magnetic potentials in dimension two
• Resolvent Estimates for Non-Self-Adjoint Magnetic Schrödinger Operators