SUM RULES FOR JACOBI MATRICES AND THEIR APPLICATIONS TO SPECTRAL THEORY

Dr. Bashir Eissa Mohammed Abdelrahman ()

Journal of Statistics and Actuarial Research, 2021, vol. 5, issue 1, 21 - 38

Abstract: The study discusses the proof of and symmetric application of Cases sum rules for Jacobi matrices. Of special interest is a linear combination of these sum rules which have strictly positive terms. The complete classification of the spectral measure of all Jacobi matrices J for which J-J0 is Hilbert space -Achmidt. The study shows the bound of a Jacobi matrix. The description for the point and absolutely continuous spectrum, while for the singular continuous spectrum additional assumptions are needed. The study shows and prove a bound of a Jacobi matrix. And we give complete description for the point and absolutely continuous spectrum, while for the singular continuous spectrum additional assumptions are needed, we prove a characterization of a characteristic function of a row contraction operator and verify its defect operator. We also prove a commutability of an operator of this row contraction.

Keywords: Sum Rules; Jacobi matrices; Spectral Theory (search for similar items in EconPapers)
Date: 2021
References: Add references at CitEc
Citations:

Downloads: (external link)
https://iprjb.org/journals/index.php/JSAR/article/view/1482 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bdu:ojjsar:v:5:y:2021:i:1:p:21-38:id:1482

Access Statistics for this article

More articles in Journal of Statistics and Actuarial Research from IPRJB
Bibliographic data for series maintained by Chief Editor ().