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Automorphisms of Algebras and Bochner's Property for Vector Orthogonal Polynomials
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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Automorphisms of Algebras and Bochner's Property for Vector Orthogonal Polynomials
Інший ID:
2010 Mathematics Subject Classification: 34L20; 30C15; 33E05
DOI:10.3842/SIGMA.2016.050
DOI:10.3842/SIGMA.2016.050
Посилання:
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.
Підтримка:
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.
Дата:
2016
Переглядів:
567
Завантажень:
254
Анотація:
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.
