02-216 \author{R. del Rio, S. Fuentes, A. Poltoratski}
\title{Coexistence of spectra in rank-one perturbation problems.} (45K, Latex2e with 2 (.bmp) figures, compressed in one file .zip) May 7, 02
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Abstract. \begin{abstract} We study the behavior of spectral functions corresponding to selfadjoint operators of the form $A + \lambda \langle \varphi, \cdot \rangle \varphi $. The focus is on the coexistence of absolutely continuous and singular spectra for values of the real parameter $\lambda $ in a given set $B$. For almost all points of $B$ it is possible to construct a family of rank one perturbations with mixed spectra. \end{abstract}

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