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arXiv · 2410.07449

New tools for the study of Bochner differential operators

L. M. Anguas·D. Barrios Rolanía
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Abstract

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 $\{δ_n^{(k)}\}$.

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L. M. Anguas, D. Barrios Rolanía. 2024-10-09. New tools for the study of Bochner differential operators. https://arxiv.org/abs/2410.07449

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