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періодичних видань НАН України
періодичних видань НАН України
Automorphisms of Algebras and Bochner's Property for Vector Orthogonal Polynomials
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- Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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| dc.contributor.author | Horozov, E. | |
| dc.date.accessioned | 2019-02-15T19:06:23Z | |
| dc.date.available | 2019-02-15T19:06:23Z | |
| dc.date.issued | 2016 | |
| dc.identifier.citation | 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. | uk_UA |
| dc.identifier.issn | 1815-0659 | |
| dc.identifier.other | 2010 Mathematics Subject Classification: 34L20; 30C15; 33E05 | |
| dc.identifier.other | DOI:10.3842/SIGMA.2016.050 | |
| dc.identifier.uri | http://dspace.nbuv.gov.ua/handle/123456789/147746 | |
| dc.description.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. | uk_UA |
| dc.description.sponsorship | This paper is a contribution to the Special Issue on Orthogonal Polynomials, Special Functions and Applications. The full collection is available at http://www.emis.de/journals/SIGMA/OPSFA2015.html. s The author is deeply grateful to Boris Shapiro for showing and discussing some examples of systems of polynomials studied here and in particular the examples from [33]. Without this probably the project would have never be even started. Also Plamen Iliev made valuable comments on some results generalizing Laguerre polynomials, which helped me to place my work among the rest of the research. Milen Yakimov pointed out several errors. Many thanks go to the referees and the editor who pointed out a number of incorrect formulas and misprints and thus helped me to improve considerably the initial text. The author is grateful to the Mathematics Department of Stockholm University for the hospitality in April 2015. Last but not least I am extremely grateful to Professors T. Tanev and K. Kostadinov, and Mrs. Z. Karova from the Bulgarian Ministry of Education and Science and Professor P. Dolashka, who helped me in the dif ficult situation when I was sacked by Sofia university in violations of the Bulgarian laws². | uk_UA |
| dc.language.iso | en | uk_UA |
| dc.publisher | Інститут математики НАН України | uk_UA |
| dc.relation.ispartof | Symmetry, Integrability and Geometry: Methods and Applications | |
| dc.title | Automorphisms of Algebras and Bochner's Property for Vector Orthogonal Polynomials | uk_UA |
| dc.type | Article | uk_UA |
| dc.status | published earlier | uk_UA |
