Oleg Safronov
The amount of discrete spectrum of a perturbed periodic Schr\"odinger 
operator inside a fixed interval $(\lambda_1,\lambda_2)$
(195K, Postscript)

ABSTRACT.  In this paper we extend the results of \cite{Sa} for a more general 
class 
of perturbations. 
 Let $A$ be a periodic Schr\"odinger operator 
 and let $V\geq0$ be a decaying potential. 
We study the number 
$ \tilde{N}(\alpha)$ 
 of the 
eigenvalues of the operator $A(\alpha)=A-\alpha V$ inside a fixed interval 
 $(\lambda_1,\lambda_2)$. We obtain an asymptotic formula for 
 $\tilde{N}(\alpha)$ 
as $\alpha\to\infty$.