Let $\{P_n(x) \}_{n=0}^\infty$ be an orthogonal polynomial system relative to a compactly supported measure. We find characterizations for $\{P_n(x) \}_{n=0}^\infty$ to be a Bochner--Krall orthogonal polynomial system, that is, $\{P_n(x) \}_{n=0}^\infty$ are polynomial eigenfunctions of a linear differential operator of finite order. In particular, we show that $\{P_n(x) \}_{n=0}^\infty$ must be generalized Jacobi polynomials which are orthogonal relative to a Jacobi weight plus two point masses.
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Communicated by Erik Koelink
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Kwon, K., Lee, D. Characterizations of Bochner–Krall Orthogonal Polynomials of Jacobi Type. Constr. Approx. 19, 599–619 (2003). https://doi.org/10.1007/s00365-003-0540-7
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DOI: https://doi.org/10.1007/s00365-003-0540-7