✦ LIBER ✦
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 + θ 〈φ , ·〉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)