Publication:
On kernel polynomials and self perturbation of orthogonal polynomials

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ISSN: 0373-3114 (Print)
ISSN: 1618-1891 (Online)
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2001-07
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Springer
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Abstract
Given an orthogonal polynomial system $(Q_n(x))_{n=0} infty$, define another polynomial system by where αn are complex numbers and t is a positive integer. We find conditions for $(P_n(x))_{n=0} infty$ to be an orthogonal polynomial system. When t=1 and α1≠0, it turns out that $(Q_n(x))_{n=0} infty$ must be kernel polynomials for $(P_n(x))_{n=0} infty$ for which we study, in detail, the location of zeros and semi-classical character.
Description
20 pages, no figures.-- MSC2000 code: 42C05.
MR#: MR1847402 (2002h:42049)
Zbl#: Zbl 1034.42022
Keywords
Kernel polynomials, Orthogonal polynomials
Bibliographic citation
Annali di Matematica Pura ed Applicata, 2001, vol. 180, n. 2, p. 127-146