Electronic Journal of Differential Equations,
Vol. 1999(1999), No. 13, pp. 1-27.

Title: Asymptotic properties of the magnetic integrated density of states   

Author: G. D. Raikov (Institute of Mathematics and Informatics, Bulgaria)
         
Abstract: This article could be regarded as a supplement to [11] 
where we considered  the Schr\"odinger operator with constant 
magnetic field and decaying electric potential, and studied  
the asymptotic behaviour of the discrete
spectrum as the coupling constant of the magnetic field tends to infinity. 
To describe this behaviour when the kernel of the 
magnetic field is not trivial, 
we introduced a  measure ${\cal D}(\lambda )$ defined on $(-\infty,0)$ 
called the ``magnetic integrated density of states''. 
In this article, we study the asymptotic behaviour of this measure  as 
$\lambda\uparrow 0$ and as $\lambda \downarrow \lambda_0$, $\lambda_0$ 
being the lower bound of the support of ${\cal D}$.


Submitted October 11, 1998. Published April 26, 1999.
Math Subject Classification: 35J10, 35P20, 81Q10.
Key Words: magnetic Schrodinger operator; integrated density of states;
           spectral asymptotics.