A Formula for Eigenvalues of Jacobi Matrices with a Reflection Symmetry
Author
Source
Advances in Mathematical Physics
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-10-16
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
The spectral properties of two special classes of Jacobi operators are studied.
For the first class represented by the 2M-dimensional real Jacobi matrices whose entries are symmetric with respect to the secondary diagonal, a new polynomial identity relating the eigenvalues of such matrices with their matrix entries is obtained.
In the limit M→∞ this identity induces some requirements, which should satisfy the scattering data of the resulting infinite-dimensional Jacobi operator in the half-line, of which super- and subdiagonal matrix elements are equal to -1.
We obtain such requirements in the simplest case of the discrete Schrödinger operator acting in l2(N), which does not have bound and semibound states and whose potential has a compact support.
American Psychological Association (APA)
Rutkevich, S. B.. 2018. A Formula for Eigenvalues of Jacobi Matrices with a Reflection Symmetry. Advances in Mathematical Physics،Vol. 2018, no. 2018, pp.1-11.
https://search.emarefa.net/detail/BIM-1119353
Modern Language Association (MLA)
Rutkevich, S. B.. A Formula for Eigenvalues of Jacobi Matrices with a Reflection Symmetry. Advances in Mathematical Physics No. 2018 (2018), pp.1-11.
https://search.emarefa.net/detail/BIM-1119353
American Medical Association (AMA)
Rutkevich, S. B.. A Formula for Eigenvalues of Jacobi Matrices with a Reflection Symmetry. Advances in Mathematical Physics. 2018. Vol. 2018, no. 2018, pp.1-11.
https://search.emarefa.net/detail/BIM-1119353
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1119353