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SIGMA, 2016, Volume 12, 050, 14 pages (Mi sigma1132)  

This article is cited in 2 scientific papers (total in 2 papers)

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

Emil Horozovab

a Institute of Mathematics and Informatics, Bulg. Acad. of Sci., Acad. G. Bonchev Str., Block 8, 1113 Sofia, Bulgaria
b Department of Mathematics and Informatics, Sofia University, 5 J. Bourchier Blvd., Sofia 1126, Bulgaria

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.

Keywords: vector orthogonal polynomials; finite recurrence relations; bispectral problem; Bochner theorem.

DOI: https://doi.org/10.3842/SIGMA.2016.050

Full text: PDF file (369 kB)
Full text: http://www.emis.de/journals/SIGMA/2016/050/
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Bibliographic databases:

ArXiv: 1512.03898
MSC: 34L20; 30C15; 33E05
Received: January 26, 2016; in final form May 12, 2016; Published online May 19, 2016
Language:

Citation: Emil Horozov, “Automorphisms of Algebras and Bochner's Property for Vector Orthogonal Polynomials”, SIGMA, 12 (2016), 050, 14 pp.

Citation in format AMSBIB
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\by Emil~Horozov
\paper Automorphisms of Algebras and Bochner's Property for Vector Orthogonal Polynomials
\jour SIGMA
\yr 2016
\vol 12
\papernumber 050
\totalpages 14
\mathnet{http://mi.mathnet.ru/sigma1132}
\crossref{https://doi.org/10.3842/SIGMA.2016.050}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84975042115}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. Horozov, “Vector orthogonal polynomials with Bochner's property”, Constr. Approx., 48:2 (2018), 201–234  crossref  mathscinet  isi  scopus
    2. E. Horozov, “$d$-Orthogonal Analogs of Classical Orthogonal Polynomials”, SIGMA, 14 (2018), 063, 27 pp.  mathnet  crossref
  • Symmetry, Integrability and Geometry: Methods and Applications
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