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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| 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| _version_ | 1862614803245170688 |
|---|---|
| author | Horozov, E. |
| author_facet | Horozov, E. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2025-11-29T12:08:35Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147746 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-29T12:08:35Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Horozov, E. 2019-02-15T19:06:23Z 2019-02-15T19:06:23Z 2016 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. 1815-0659 2010 Mathematics Subject Classification: 34L20; 30C15; 33E05 DOI:10.3842/SIGMA.2016.050 https://nasplib.isofts.kiev.ua/handle/123456789/147746 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Automorphisms of Algebras and Bochner's Property for Vector Orthogonal Polynomials Article published earlier |
| spellingShingle | Automorphisms of Algebras and Bochner's Property for Vector Orthogonal Polynomials Horozov, E. |
| title | Automorphisms of Algebras and Bochner's Property for Vector Orthogonal Polynomials |
| title_full | Automorphisms of Algebras and Bochner's Property for Vector Orthogonal Polynomials |
| title_fullStr | Automorphisms of Algebras and Bochner's Property for Vector Orthogonal Polynomials |
| title_full_unstemmed | Automorphisms of Algebras and Bochner's Property for Vector Orthogonal Polynomials |
| title_short | Automorphisms of Algebras and Bochner's Property for Vector Orthogonal Polynomials |
| title_sort | automorphisms of algebras and bochner's property for vector orthogonal polynomials |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147746 |
| work_keys_str_mv | AT horozove automorphismsofalgebrasandbochnerspropertyforvectororthogonalpolynomials |