Structure of operator algebras for matrix orthogonal polynomials
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866911148533612544 |
|---|---|
| author | Parisi, Ignacio Bono Pacharoni, Inés |
| author_facet | Parisi, Ignacio Bono Pacharoni, Inés |
| contents | In this paper, we study the structure of the differential operator algebra \( \mathcal{D}(W) \) and its associated eigenvalue algebra \( Λ(W) \) for matrix-valued orthogonal polynomials. While \( Λ(W) \) is isomorphic to \( \mathcal{D}(W) \), its simpler framework allows us to efficiently derive strong results about \( \mathcal{D}(W) \) and its center \( \mathcal{Z}(W) \). We analyze the behavior of the center under Darboux transformations, establishing explicit relationships between the centers of Darboux-equivalent weights. These results are illustrated through the study of both reducible and irreducible matrix weights, including a detailed analysis of an irreducible Jacobi-type weight. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_16070 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Structure of operator algebras for matrix orthogonal polynomials Parisi, Ignacio Bono Pacharoni, Inés Classical Analysis and ODEs Operator Algebras 33C45, 42C05, 34L05, 34L10 In this paper, we study the structure of the differential operator algebra \( \mathcal{D}(W) \) and its associated eigenvalue algebra \( Λ(W) \) for matrix-valued orthogonal polynomials. While \( Λ(W) \) is isomorphic to \( \mathcal{D}(W) \), its simpler framework allows us to efficiently derive strong results about \( \mathcal{D}(W) \) and its center \( \mathcal{Z}(W) \). We analyze the behavior of the center under Darboux transformations, establishing explicit relationships between the centers of Darboux-equivalent weights. These results are illustrated through the study of both reducible and irreducible matrix weights, including a detailed analysis of an irreducible Jacobi-type weight. |
| title | Structure of operator algebras for matrix orthogonal polynomials |
| topic | Classical Analysis and ODEs Operator Algebras 33C45, 42C05, 34L05, 34L10 |
| url | https://arxiv.org/abs/2502.16070 |