On Kernel polynomials and self-perturbation of orthogonal polynomials |
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| Authors: | KH Kwon DW Lee F Marcellán SB Park |
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| Institution: | (1) Division of Applied Mathematics, KAIST, Taejon 305-701, Korea, e-mail: khkwon@jacobi.kaist.ac.kr, KR;(2) Dept. of Math., Teachers College, Kyungpook National University, Taegu 702-701, Korea, e-mail: dwlee@gauss.knu.ac.kr, KR;(3) Dept. de Matematicas, Univ. Carlos III, Avenida Universidad 30, Leganés-Madrid, Spain, e-mail: pacomarc@ing.uc3m.es, ES;(4) Dept. of Mathematics, Korean Military Academy, Seoul 139-799, Korea, KR |
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| Abstract: | Given an orthogonal polynomial system {Q
n
(x)}
n=0
∞, define another polynomial system by where α
n
are complex numbers and t is a positive integer. We find conditions for {P
n
(x)}
n=0
∞ to be an orthogonal polynomial system. When t=1 and α1≠0, it turns out that {Q
n
(x)}
n=0
∞ must be kernel polynomials for {P
n
(x)}
n=0
∞ for which we study, in detail, the location of zeros and semi-classical character.
Received: November 25, 1999; in final form: April 6, 2000?Published online: June 22, 2001 |
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| Keywords: | : kernel polynomials – orthogonal polynomials |
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