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Decompositions of Singular Continuous Spectra ofmathcal{H}_{ - 2} -class Rank One Perturbations |
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| Authors: | Sergio Albeverio Alexei Konstantinov Volodymyr Koshmanenko |
| Affiliation: | (1) Institut für Angewandte Mathematik, Universität Bonn, Wegelerstr. 6, D-53115 Bonn, Germany;(2) SFB 611, Bonn, Germany;(3) BiBoS, Bielefeld, Bonn, Germany;(4) IZKS, Bonn, Germany;(5) CERFIM, Locarno, Switzerland;(6) ACC Arch., Mendrisio, Switzerland;(7) Department of Mathematics, Kyiv University, 64 Volodymyrs’ka str., 01033 Kyiv, Ukraine;(8) Institute of Mathematics, National Academy of Sciences, 3 Tereshchenkivs’ka str., 01601 Kyiv, Ukraine |
| Abstract: | The decomposition theory for the singular continuous spectrum of rank one singular perturbations is studied. A generalization of the well-known Aronszajn-Donoghue theory to the case of decompositions with respect to α-dimensional Hausdorff measures is given and a characterization of the supports of the α-singular, α-absolutely continuous, and strongly α-continuous parts of the spectral measure of - class rank one singular perturbations is given in terms of the limiting behaviour of the regularized Borel transform. |
| Keywords: | Primary 47A10 Secondary 47A55 |
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