**
Below is the ascii version of the abstract for 03-535.
The html version should be ready soon.**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}