期刊
JOURNAL OF APPROXIMATION THEORY
卷 182, 期 -, 页码 29-58出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jat.2014.03.004
关键词
Orthogonal polynomials; Exceptional orthogonal polynomial; Difference operators; Differential operators; Charlier polynomials; Hermite polynomials
类别
资金
- Ministerio de Economia y Competitividad [MTM2012-36732-C03-03]
- Junta de Andalucia [FQM-262, FQM-4643, FQM-7276]
- Feder Funds (European Union)
Using Casorati determinants of Charlier polynomials (C-n(a))(n), we construct for each finite set F of positive integers a sequence of polynomials C-n,(a) n is an element of F-sigma, which are eigenfunctions of a second order difference operator, where F-sigma is certain infinite set of nonnegative integers, sigma F not subset of N. For suitable finite sets F (we call them admissible sets), we prove that the polynomials C-n,(a) n is an element of F-sigma, are actually exceptional Charlier polynomials; that is, in addition, they are orthogonal and complete with respect to a positive measure. By passing to the limit, we transform the Casorati determinant of Charlier polynomials into a Wronskian determinant of Hermite polynomials. For admissible sets, these Wronskian determinants turn out to be exceptional Hermite polynomials. (C) 2014 Elsevier Inc. All rights reserved.
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