Rank one perturbations of Jacobi matrices with mixed spectra | Zendy

del Rio R. | Zendy; Kudryavtsev M. | Zendy; Silva L. | Zendy

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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

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)

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