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,...
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| Опубліковано в: : | Український математичний вісник |
|---|---|
| Дата: | 2018 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2018
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/169420 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862708433508106240 |
|---|---|
| author | Kovalyov, I.M. |
| author_facet | Kovalyov, I.M. |
| 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. |
| collection | DSpace DC |
| container_title | Український математичний вісник |
| 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.
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| first_indexed | 2025-12-07T17:10:51Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-169420 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1810-3200 |
| language | English |
| last_indexed | 2025-12-07T17:10:51Z |
| publishDate | 2018 |
| publisher | Інститут прикладної математики і механіки НАН України |
| 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 |
| spellingShingle | Shifted Darboux transformations of the generalized Jacobi matrices, I Kovalyov, I.M. |
| title | 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_short | Shifted Darboux transformations of the generalized Jacobi matrices, I |
| title_sort | shifted darboux transformations of the generalized jacobi matrices, i |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/169420 |
| work_keys_str_mv | AT kovalyovim shifteddarbouxtransformationsofthegeneralizedjacobimatricesi |