R. del Rio, M. Kudryavtsev
Rank One Perturbations of Jacobi Matrices with Mixed Spectra
(336K, Postscript)

ABSTRACT.  We study spectral properties of rank one perturbations of selfadjoint 
operators 
$$ A_{\lambda } = A + \lambda < \varphi , \cdot > \varphi $$ 
\noindent in relation to their dependence on the real parameter 
$\lambda $. For semi infinite Jacobi matrices criteria is given that 
guarantees existence of mixed spectral types for sets of positive 
measure in the coupling constant $\lambda $ when the unperturbed 
operator has a potential which vanishes in a finite interval. 
\end{abstract}