 01236 S.A. Denisov
 On the existence of the absolutely continuous component for the spectral
measure associated with some Krein systems and SturmLiouville operators.
(36K, LATeX)
Jul 2, 01

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. We consider SturmLiouville operators and Krein systems.
For Krein systems, we study the behavior of generalized
polynomials at the infinity for spectral parameters in the
upper halfplain. That makes it possible to establish the
presence of absolutely continuous component of the associated
measure. For SturmLiouville operator on the halfline 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.
 Files:
01236.src(
01236.keywords ,
Mnv1.tex )