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Perturbations of Jacobi polynomials and piece-wise hypergeometric orthogonal systems

Yurii A. Neretin
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Abstract

We construct noncomplete orthogonal systems on the ray $[0,\infty)$ that look like Jacobi polynomials $P_n(x)$ after a shift of degree $n\mapsto n+a$, where $a$ is a real constant. These systems are solutions of some exotic Sturm-Liouville problem for hypergeometric differential operators. We obtain the explicit spectral decomposition for these problems.

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Yurii A. Neretin. 2005-05-10. Perturbations of Jacobi polynomials and piece-wise hypergeometric orthogonal systems. https://doi.org/10.4213/sm1146, 10.1070/sm2006v197n11abeh003815

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