Shifted Darboux transformations of the generalized Jacobi matrices, I

• Published in: Український математичний вісник
• Date: 2018
• ISSN: 1810-3200
• Main Author: Kovalyov, I.M.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2018
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/169420
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Shifted Darboux transformations of the generalized Jacobi matrices, I / I.M. Kovalyov // Український математичний вісник. — 2018. — Т. 15, № 4. — С. 490-515. — Бібліогр.: 26 назв. — англ.

Let J be a monic generalized Jacobi matrix, i.e., a three-diagonal block matrix of a special form. We find conditions for a monic generalized Jacobi matrix J to admit a factorization J = LU + αI with L and U being lower and upper triangular two-diagonal block matrices of special forms. In this case,...