This article is cited in 5 papers

Automorphisms of Algebras and Bochner's Property for Vector Orthogonal Polynomials

Emil Horozov<sup>ab

a</sup> Institute of Mathematics and Informatics, Bulg. Acad. of Sci., Acad. G. Bonchev Str., Block 8, 1113 Sofia, Bulgaria
^b Department of Mathematics and Informatics, Sofia University, 5 J. Bourchier Blvd., Sofia 1126, Bulgaria

Abstract: 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.

MSC: 34L20; 30C15; 33E05

Received: January 26, 2016; in final form May 12, 2016; Published online May 19, 2016

Language: English

DOI: 10.3842/SIGMA.2016.050

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ArXiv: 1512.03898