Resolvent estimates for the magnetic Hamiltonian with singular vector potentials and applications

Abstract

For the magnetic Hamiltonian with singular vector potentials, we analytically continue the resolvent to a logarithmic neighborhood of the positive real axis and prove resolvent estimates there. As applications, we obtain asymptotic locations of resonances and a local smoothing estimate for solutions of the corresponding Schrödinger equation.

v2: 21 pages, 2 figures, to appear in Communications in Mathematical Physics

References in corpus (3)

• Diffraction of the Aharonov-Bohm Hamiltonian
• The wave trace and resonances of the magnetic Hamiltonian with singular vector potentials
• Dispersive estimates for 2D-wave equations with critical potentials