S.A. Denisov
On the existence of the absolutely continuous component for the spectral 
measure associated with some Krein systems and Sturm-Liouville operators.
(36K, LATeX)

ABSTRACT.   We consider Sturm-Liouville operators and Krein systems. 
For Krein systems, we study the behavior of generalized 
polynomials at the infinity for spectral parameters in the 
upper half-plain. That makes it possible to establish the 
presence of absolutely continuous component of the associated 
measure. For Sturm-Liouville operator on the half-line with 
bounded potential, we prove that the essential support of the 
absolutely continuous component of the spectral measure is 
$[m,\infty)$ if $\limsup_{x\to\infty} q(x)=m$ and 
$q^{\prime}\in L^2(R^+)$. That holds for arbitrary conditions 
at zero. This result partially solves one open problem stated 
recently by S.Molchanov, M.Novitskii, and B.Vainberg.