Darboux equivalence for matrix-valued orthogonal polynomials
| Title: | Darboux equivalence for matrix-valued orthogonal polynomials |
|---|---|
| Authors: | Parisi, Ignacio Bono, Pacharoni, Inés, Zurrián, Ignacio |
| Publication Year: | 2024 |
| Collection: | Mathematics |
| Subject Terms: | Mathematics - Classical Analysis and ODEs, 33C45, 42C05, 33C47 |
| More Details: | 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. |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/2407.20994 |
| Accession Number: | edsarx.2407.20994 |
| Database: | arXiv |
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