03-535 R. del Rio, M. Kudryavtsev

Rank One Perturbations of Jacobi Matrices with Mixed Spectra (336K, Postscript) Dec 10, 03

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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}

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