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A Bochner type characterization theorem for exceptional orthogonal polynomials.
- Source :
-
Journal of Mathematical Analysis & Applications . Apr2019, Vol. 472 Issue 1, p584-626. 43p. - Publication Year :
- 2019
-
Abstract
- Abstract It was recently conjectured that every system of exceptional orthogonal polynomials is related to a classical orthogonal polynomial system by a sequence of Darboux transformations. In this paper we prove this conjecture, which paves the road to a complete classification of all exceptional orthogonal polynomials. In some sense, this paper can be regarded as the extension of Bochner's result for classical orthogonal polynomials to the exceptional class. As a supplementary result, we derive a canonical form for exceptional operators based on a bilinear formalism, and prove that every exceptional operator has trivial monodromy at all primary poles. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0022247X
- Volume :
- 472
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 133623324
- Full Text :
- https://doi.org/10.1016/j.jmaa.2018.11.042