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Construction of differential operators having Bochner-Krall orthogonal polynomials as eigenfunctions. (English) Zbl 1121.34016
Authors’ abstract: Suppose ${\left\{{Q}_{n}\right\}}_{n=0}^{\infty }$ 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 ${\left\{{Q}_{n}\right\}}_{n=0}^{\infty }$ as eigenfunctions.
##### MSC:
 34A55 Inverse problems of ODE 34L05 General spectral theory for OD operators 34L10 Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions (ODE)
##### Keywords:
Magnus’ conjecture