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

Symmetry Integrability and Geometry-Methods and Applications

article

Emil Horozov¹ 

[1] Department of Mathematics and Informatics, Sofia University

关键词: vector orthogonal polynomials;    finite recurrence relations;    bispectral problem;    Bochner theorem;   

DOI  :  10.3842/SIGMA.2016.050

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown