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Rank one perturbations of Jacobi matrices with mixed spectra
Author(s) -
del Rio R.,
Kudryavtsev M.,
Silva L.
Publication year - 2006
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310375
Subject(s) - mathematics , spectral measure , rank (graph theory) , lebesgue measure , measure (data warehouse) , pure mathematics , lebesgue integration , operator (biology) , spectral properties , spectral line , set (abstract data type) , work (physics) , mathematical analysis , combinatorics , computational chemistry , chemistry , quantum mechanics , physics , gene , biochemistry , repressor , database , computer science , transcription factor , programming language
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 AA θ = A + θ 〈 φ , ·〉 φin 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)