The CMV bispectrality of the Jacobi polynomials on the unit circle
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913611769708544 |
|---|---|
| author | Vinet, Luc Zhedanov, Alexei |
| author_facet | Vinet, Luc Zhedanov, Alexei |
| contents | We show that the Jacobi polynomials that are orthogonal on the unit circle (the Jacobi OPUC) are CMV bispectral. This means that the corresponding Laurent polynomials in the CMV basis satisfy two dual ordinary eigenvalue problems: a recurrence relation and a differential equation of Dunkl type. This is presumably the first nontrivial explicit example of CMV bispectral OPUC. We introduce the circle Jacobi algebra which plays the role of hidden symmetry algebra for the Jacobi OPUC. All fundamental properties of the Jacobi OPUC can be derived from representations of this algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_11031 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The CMV bispectrality of the Jacobi polynomials on the unit circle Vinet, Luc Zhedanov, Alexei Classical Analysis and ODEs 33C45 We show that the Jacobi polynomials that are orthogonal on the unit circle (the Jacobi OPUC) are CMV bispectral. This means that the corresponding Laurent polynomials in the CMV basis satisfy two dual ordinary eigenvalue problems: a recurrence relation and a differential equation of Dunkl type. This is presumably the first nontrivial explicit example of CMV bispectral OPUC. We introduce the circle Jacobi algebra which plays the role of hidden symmetry algebra for the Jacobi OPUC. All fundamental properties of the Jacobi OPUC can be derived from representations of this algebra. |
| title | The CMV bispectrality of the Jacobi polynomials on the unit circle |
| topic | Classical Analysis and ODEs 33C45 |
| url | https://arxiv.org/abs/2412.11031 |