Darboux equivalence for matrix-valued orthogonal polynomials
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914183343243264 |
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| author | Parisi, Ignacio Bono Pacharoni, Inés Zurrián, Ignacio |
| author_facet | Parisi, Ignacio Bono Pacharoni, Inés Zurrián, Ignacio |
| contents | In this work, we give some criteria that allow us to decide when two sequences of matrix-valued orthogonal polynomials are related via a Darboux transformation and to build explicitly such transformation. In particular, they allow us to see when and how any given sequence of polynomials is Darboux related to a diagonal matrix of classic orthogonal polynomials. We also explore the notion of Darboux-irreducibility and study some sequences that are not a Darboux transformation of classical orthogonal polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20994 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Darboux equivalence for matrix-valued orthogonal polynomials Parisi, Ignacio Bono Pacharoni, Inés Zurrián, Ignacio Classical Analysis and ODEs 33C45, 42C05, 33C47 In this work, we give some criteria that allow us to decide when two sequences of matrix-valued orthogonal polynomials are related via a Darboux transformation and to build explicitly such transformation. In particular, they allow us to see when and how any given sequence of polynomials is Darboux related to a diagonal matrix of classic orthogonal polynomials. We also explore the notion of Darboux-irreducibility and study some sequences that are not a Darboux transformation of classical orthogonal polynomials. |
| title | Darboux equivalence for matrix-valued orthogonal polynomials |
| topic | Classical Analysis and ODEs 33C45, 42C05, 33C47 |
| url | https://arxiv.org/abs/2407.20994 |