Bispectrality for matrix Laguerre-Sobolev polynomials
In this contribution we deal with sequences of polynomials orthogonal with respect to a Sobolev type inner product. A banded symmetric operator is associated with such a sequence of polynomials according to the higher order difference equation they satisfy. Taking into account the Darboux transforma...
| Authors: | ; |
|---|---|
| Format: | Article |
| Status: | Submitted version |
| Publication date: | 2024 |
| Country: | España |
| Institution: | Universidad de Sevilla (US) |
| Repository: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/160562 |
| Online Access: | https://hdl.handle.net/11441/160562 https://doi.org/10.1016/j.laa.2023.09.017 |
| Access Level: | Open access |
| Keyword: | Standard orthogonal polynomials Sobolev type orthogonal polynomials Darboux transformations Matrix orthogonal polynomials Bispectrality |
| _version_ | 1878735540662042625 |
|---|---|
| author | Marcellán Español, Francisco |
| author2 | Zurrián, Ignacio Nahuel |
| author2_role | author |
| author_browse | Marcellán Español, Francisco Zurrián, Ignacio Nahuel |
| author_facet | Marcellán Español, Francisco Zurrián, Ignacio Nahuel |
| author_role | author |
| collection | idUS. Depósito de Investigación de la Universidad de Sevilla |
| description | In this contribution we deal with sequences of polynomials orthogonal with respect to a Sobolev type inner product. A banded symmetric operator is associated with such a sequence of polynomials according to the higher order difference equation they satisfy. Taking into account the Darboux transformation of the corresponding matrix we deduce the connection with a sequence of orthogonal polynomials associated with a Christoffel perturbation of the measure involved in the standard part of the Sobolev inner product. A connection with matrix orthogonal polynomials is stated. The Laguerre-Sobolev type case is studied as an illustrative example. Finally, the bispectrality of such matrix orthogonal polynomials is pointed out. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_7ebbefce4f5c28fa73bda88ae2e8ca1a |
| institution | Universidad de Sevilla (US) |
| instname_str | Universidad de Sevilla (US) |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:idus.us.es:11441/160562 |
| publishDate | 2024 |
| publishDateSort | 2024 |
| publisher | Elsevier |
| publisherStr | Elsevier |
| reponame_str | idUS. Depósito de Investigación de la Universidad de Sevilla |
| spelling | Bispectrality for matrix Laguerre-Sobolev polynomials Marcellán Español, Francisco Zurrián, Ignacio Nahuel Standard orthogonal polynomials Sobolev type orthogonal polynomials Darboux transformations Matrix orthogonal polynomials Bispectrality In this contribution we deal with sequences of polynomials orthogonal with respect to a Sobolev type inner product. A banded symmetric operator is associated with such a sequence of polynomials according to the higher order difference equation they satisfy. Taking into account the Darboux transformation of the corresponding matrix we deduce the connection with a sequence of orthogonal polynomials associated with a Christoffel perturbation of the measure involved in the standard part of the Sobolev inner product. A connection with matrix orthogonal polynomials is stated. The Laguerre-Sobolev type case is studied as an illustrative example. Finally, the bispectrality of such matrix orthogonal polynomials is pointed out. Elsevier https://hdl.handle.net/11441/160562 https://doi.org/10.1016/j.laa.2023.09.017 |
| spellingShingle | Bispectrality for matrix Laguerre-Sobolev polynomials Marcellán Español, Francisco Standard orthogonal polynomials Sobolev type orthogonal polynomials Darboux transformations Matrix orthogonal polynomials Bispectrality |
| status_str | submittedVersion |
| title | Bispectrality for matrix Laguerre-Sobolev polynomials |
| title_full | Bispectrality for matrix Laguerre-Sobolev polynomials |
| title_fullStr | Bispectrality for matrix Laguerre-Sobolev polynomials |
| title_full_unstemmed | Bispectrality for matrix Laguerre-Sobolev polynomials |
| title_short | Bispectrality for matrix Laguerre-Sobolev polynomials |
| title_sort | Bispectrality for matrix Laguerre-Sobolev polynomials |
| topic | Standard orthogonal polynomials Sobolev type orthogonal polynomials Darboux transformations Matrix orthogonal polynomials Bispectrality |
| topic_facet | Standard orthogonal polynomials Sobolev type orthogonal polynomials Darboux transformations Matrix orthogonal polynomials Bispectrality |
| url | https://hdl.handle.net/11441/160562 https://doi.org/10.1016/j.laa.2023.09.017 |