Automorphisms of Algebras and Bochner's Property for Vector Orthogonal Polynomials
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 constructe...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2016 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2016
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147746 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Automorphisms of Algebras and Bochner's Property for Vector Orthogonal Polynomials / E. Horozov // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 36 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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.
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| ISSN: | 1815-0659 |