Perturbations of Jacobi polynomials and piece-wise hypergeometric orthogonal systems

الأصل · EN

We construct noncomplete orthogonal systems on the ray [0,∞) that look like Jacobi polynomials Pₙ(x) after a shift of degree n 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.