Evgeni Korotyaev, Alexander Pushnitski
A trace formula and high energy spectral asymptotics for the perturbed Landau Hamiltonian
(71K, Latex2e)

ABSTRACT.  A two-dimensional Schr\"odinger operator with a constant 
magnetic field perturbed by a smooth compactly supported potential 
is considered. The spectrum of this operator consists of 
eigenvalues which accumulate to the Landau levels. 
We call the set of eigenvalues near the $n$'th Landau level 
an $n$'th eigenvalue cluster, and study the distribution of 
eigenvalues in the $n$'th cluster as $n\to\infty$. 
A complete asymptotic expansion for the eigenvalue moments 
in the $n$'th cluster is obtained and some coefficients 
of this expansion are computed. A trace formula involving the 
first eigenvalue moments is obtained.