Shifted Darboux transformations of the generalized Jacobi matrices, I
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,...
Gespeichert in:
| Veröffentlicht in: | Український математичний вісник |
|---|---|
| Datum: | 2018 |
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2018
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/169420 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-169420 |
|---|---|
| record_format |
dspace |
| spelling |
Kovalyov, I.M. 2020-06-12T19:20:29Z 2020-06-12T19:20:29Z 2018 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. 1810-3200 2010 MSC. Primary 47B36; Secondary 47B50; 42C05; 15A23 https://nasplib.isofts.kiev.ua/handle/123456789/169420 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, the shifted parameterless Darboux transformation of J defined by J(p) = UL+αI is shown to be also a monic generalized Jacobi matrix. Analogs of the Christoffel formulas for polynomials of the first and second kinds corresponding to the Darboux transformation J(p) are found. en Інститут прикладної математики і механіки НАН України Український математичний вісник Shifted Darboux transformations of the generalized Jacobi matrices, I Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Shifted Darboux transformations of the generalized Jacobi matrices, I |
| spellingShingle |
Shifted Darboux transformations of the generalized Jacobi matrices, I Kovalyov, I.M. |
| title_short |
Shifted Darboux transformations of the generalized Jacobi matrices, I |
| title_full |
Shifted Darboux transformations of the generalized Jacobi matrices, I |
| title_fullStr |
Shifted Darboux transformations of the generalized Jacobi matrices, I |
| title_full_unstemmed |
Shifted Darboux transformations of the generalized Jacobi matrices, I |
| title_sort |
shifted darboux transformations of the generalized jacobi matrices, i |
| author |
Kovalyov, I.M. |
| author_facet |
Kovalyov, I.M. |
| publishDate |
2018 |
| language |
English |
| container_title |
Український математичний вісник |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| description |
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, the shifted parameterless Darboux transformation of J defined by J(p) = UL+αI is shown to be also a monic generalized Jacobi matrix. Analogs of the Christoffel formulas for polynomials of the first and second kinds corresponding to the Darboux transformation J(p) are found.
|
| issn |
1810-3200 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/169420 |
| citation_txt |
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. |
| work_keys_str_mv |
AT kovalyovim shifteddarbouxtransformationsofthegeneralizedjacobimatricesi |
| first_indexed |
2025-12-07T17:10:51Z |
| last_indexed |
2025-12-07T17:10:51Z |
| _version_ |
1850870282262151168 |