Sharp Spectral Asymptotics for 2-dimensional Schrödinger operator with a strong but degenerating magnetic field. II

2006/03/04 by Ivrii, Victor
#35P20 #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.math/0603117

Abstract

I consider the same operator as in part I assuming however that μ≥ Ch^-1 and V is replaced by (2l+1)μh F+W with l∈ \bZ⁺. Under some non-degeneracy conditions I recover remainder estimates up to O (μ^-\frac 1 νh^-1 +1) but now case μ≥ Ch^-ν is no more forbidden and the principal part is of magnitude μh^-1.

Related

• Sharp Spectral Asymptotics for 2-dimensional Schrödinger operator with a strong magnetic field. Note about forgotten generic case
• Sharp Spectral Asymptotics for two-dimensional Schrödinger operator with a strong degenerating magnetic field
• Schroedinger Operator with Strong Magnetic Field: Propagation of singularities and sharper asymptotics
• Sharp Spectral Asymptotics for Operators with Irregular Coefficients. IV. Multidimensional Schroedinger operator with a strong magnetic field. Full-rank case
• Schroedinger Operator with Strong Magnetic Field near Boundary