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Automorphisms of Algebras and Bochner's Property for Vector Orthogonal Polynomials
Symmetry, integrability and geometry: methods and applications, Tome 12 (2016) Cet article a éte moissonné depuis la source Math-Net.Ru

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We construct new families of vector orthogonal polynomials that have the property to be eigenfunctions of some differential operator. They are extensions of the Hermite and Laguerre polynomial systems. A third family, whose first member has been found by Y. Ben Cheikh and K. Douak is also constructed. The ideas behind our approach lie in the studies of bispectral operators. We exploit automorphisms of associative algebras which transform elementary vector orthogonal polynomial systems which are eigenfunctions of a differential operator into other systems of this type.
Keywords: vector orthogonal polynomials; finite recurrence relations; bispectral problem; Bochner theorem. 
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     author = {Emil Horozov},
     title = {Automorphisms of {Algebras} and {Bochner's} {Property} for {Vector} {Orthogonal} {Polynomials}},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a49/}
}
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Emil Horozov. Automorphisms of Algebras and Bochner's Property for Vector Orthogonal Polynomials. Symmetry, integrability and geometry: methods and applications, Tome 12 (2016). http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a49/

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