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A unified construction of generalized classical polynomials associated with operators of Calogero-Sutherland type. (English) Zbl 1193.33028
This paper deals with a large class of many-variable polynomials which contains generalizations of the classical Hermite, Laguerre, Jacobi and Bessel polynomials as special cases, and which occur as the polynomial part in the eigenfunctions of CalogeroSutherland type operators and their deformations recently found and studied by Chalykh, Feigin, Sergeev and Veselov. A unified and explicit construction of these polynomials is given. The construction of reduced eigenfunction of these operators is only valid under certain non-degeneracy conditions on the corresponding eigenvalues. Completeness for deformed Calogero-Sutherland operators is also discussed.

MSC:
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
33E30 Other functions coming from differential, difference and integral equations
42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
70F10 \(n\)-body problems
81U15 Exactly and quasi-solvable systems arising in quantum theory
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