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Construction of differential operators having Bochner-Krall orthogonal polynomials as eigenfunctions. (English) Zbl 1121.34016
Authors’ abstract: Suppose ${\{Q_n\}}_{n=0}^{\infty}$ is a sequence of polynomials othogonal with respect to the moment functional $\tau = \sigma + \nu$, where $\sigma$ is a classical moment functional (Jacobi, Laguerre, Hermite) and $\nu$ is a point mass distribution with finite support. In this paper, we develop a new method for constructing a differential equation having ${\{Q_n\}}_{n=0}^{\infty}$ as eigenfunctions.

MSC:
34A55Inverse problems of ODE
34L05General spectral theory for OD operators
34L10Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions (ODE)
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References:
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