Electron.n. J. Diff. Eqns., Vol. 1999(1999), No. 13, pp. 1-27.
### Asymptotic properties of the magnetic integrated density of states

G. D. Raikov

**Abstract:**

This article could be regarded as a supplement to [11]
where we considered the Schrodinger 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
defined on
called the ``magnetic integrated density of states''.
In this article, we study the asymptotic behaviour of this measure as
and as
,
being the lower bound of the support of
.
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.

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Georgi D. Raikov

Section of Mathematical Physics

Institute of Mathematics and Informatics

Bulgarian Academy of Sciences

Acad. G. Bonchev Str., bl.8, 1113 Sofia, Bulgaria

e-mail: gdraikov@omega.bg

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