$2\times 2$ Laguerre-type differential operator with triangular eigenvalue
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909398148841472 |
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| author | Gonzalez, Yanina Torres, Victoria |
| author_facet | Gonzalez, Yanina Torres, Victoria |
| contents | In this paper, we present a comprehensive account of all Laguerre-type differential operators $D$ that are symmetric with respect to a $2\times 2$ irreducible weight $W$ on the interval $(0, \infty)$. These operators are associated with monic orthogonal polynomials ${P_n}$, which satisfy the equation $DP_n = P_nΔ_n$ for a certain lower triangular eigenvalue $Δ_n$. We introduce three distinct families of operators and weights, each characterized by explicit expressions depending on two or three parameters, along with a new expression based on a single parameter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13736 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $2\times 2$ Laguerre-type differential operator with triangular eigenvalue Gonzalez, Yanina Torres, Victoria Classical Analysis and ODEs In this paper, we present a comprehensive account of all Laguerre-type differential operators $D$ that are symmetric with respect to a $2\times 2$ irreducible weight $W$ on the interval $(0, \infty)$. These operators are associated with monic orthogonal polynomials ${P_n}$, which satisfy the equation $DP_n = P_nΔ_n$ for a certain lower triangular eigenvalue $Δ_n$. We introduce three distinct families of operators and weights, each characterized by explicit expressions depending on two or three parameters, along with a new expression based on a single parameter. |
| title | $2\times 2$ Laguerre-type differential operator with triangular eigenvalue |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2411.13736 |