Perturbations of Jacobi polynomials and piece-wise hypergeometric orthogonal systems

Details Perturbations of Jacobi polynomials and piece-wise hypergeometric orthogonal systems Perturbations of Jacobi polynomials and piece-wise hypergeometric orthogonal systems

2005-05-10

arxiv.org/abs/math/0505188v2

Mathematics

Classical Analysis and ODEs

22 pages

Scientific paper

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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