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Rank one perturbations of Jacobi matrices with mixed spectra

✍ Scribed by R. del Rio; M. Kudryavtsev; L. Silva


Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
155 KB
Volume
279
Category
Article
ISSN
0025-584X

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✦ Synopsis


Abstract

Let A be a self‐adjoint operator and φ its cyclic vector. In this work we study spectral properties of rank one perturbations of A

A~θ~ = A + θφ , ·〉φ

in relation to their dependence on the real parameter θ . We find bounds on averages of spectral measures for semi‐infinite Jacobi matrices and give criteria which guarantee existence of mixed spectral types for θ in a set of positive Lebesgue measure. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)