A Class of Matrix Schrödinger Bispectral Operators
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913219551952896 |
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| author | Campos, Brian D. Vasquez |
| author_facet | Campos, Brian D. Vasquez |
| contents | We prove the bispectrality of some class of matrix Schrödinger operators with polynomial potentials that satisfy a second-order matrix autonomous differential equation. The physical equation is constructed using the formal theory of the Laurent series and after that obtaining local solutions using estimations in the Frobenius norm. Furthermore, the characterization of the algebra of polynomial eigenvalues in the spectral variable is given using some family of functions $\left\{ P_{k}\right\}_{k\in \mathbb{N}}$ with the remarkable property of satisfying a general version of the Leibniz rule. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16295 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Class of Matrix Schrödinger Bispectral Operators Campos, Brian D. Vasquez Spectral Theory Operator Algebras 35A35 47Fxx 16Dxx We prove the bispectrality of some class of matrix Schrödinger operators with polynomial potentials that satisfy a second-order matrix autonomous differential equation. The physical equation is constructed using the formal theory of the Laurent series and after that obtaining local solutions using estimations in the Frobenius norm. Furthermore, the characterization of the algebra of polynomial eigenvalues in the spectral variable is given using some family of functions $\left\{ P_{k}\right\}_{k\in \mathbb{N}}$ with the remarkable property of satisfying a general version of the Leibniz rule. |
| title | A Class of Matrix Schrödinger Bispectral Operators |
| topic | Spectral Theory Operator Algebras 35A35 47Fxx 16Dxx |
| url | https://arxiv.org/abs/2401.16295 |