New tools for the study of Bochner differential operators
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913540017750016 |
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| author | Anguas, L. M. Rolanía, D. Barrios |
| author_facet | Anguas, L. M. Rolanía, D. Barrios |
| contents | A sequence $\{δ_n^{(k)}\}$ associated to a Bochner differential operator is introduced as an effective tool to study this kind of operators. Some properties of this sequence are proven and used to deduce that a particular operator leads to solutions of a bispectral problem. In addition, the inverse problem is studied; that is, given a sequence
$\{λ_n\}$ of complex numbers and a sequence
$\{P_n\}$ of polynomials with complex coefficients,
$°{P_n}=n$, we find a necessary and sufficient condition for the existence of a Bochner differential operator that has those sequences as eigenvalues and eigenpolynomials, respectively. The mentioned condition also depends on
$\{δ_n^{(k)}\}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07449 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New tools for the study of Bochner differential operators Anguas, L. M. Rolanía, D. Barrios Functional Analysis 33C45, 34L10, 39A70 A sequence $\{δ_n^{(k)}\}$ associated to a Bochner differential operator is introduced as an effective tool to study this kind of operators. Some properties of this sequence are proven and used to deduce that a particular operator leads to solutions of a bispectral problem. In addition, the inverse problem is studied; that is, given a sequence $\{λ_n\}$ of complex numbers and a sequence $\{P_n\}$ of polynomials with complex coefficients, $°{P_n}=n$, we find a necessary and sufficient condition for the existence of a Bochner differential operator that has those sequences as eigenvalues and eigenpolynomials, respectively. The mentioned condition also depends on $\{δ_n^{(k)}\}$. |
| title | New tools for the study of Bochner differential operators |
| topic | Functional Analysis 33C45, 34L10, 39A70 |
| url | https://arxiv.org/abs/2410.07449 |