1. On kernel polynomials and self perturbation of orthogonal polynomials
- Author
-
S.B. Park, D. W. Lee, Francisco Marcellán, and K.H. Kwon
- Subjects
Classical orthogonal polynomials ,Discrete mathematics ,Combinatorics ,Polynomial ,Orthogonal polynomials ,Matemáticas ,Applied Mathematics ,Discrete orthogonal polynomials ,Kernel polynomials ,Perturbation (astronomy) ,Complex number ,Mathematics - Abstract
20 pages, no figures.-- MSC2000 code: 42C05. MR#: MR1847402 (2002h:42049) Zbl#: Zbl 1034.42022 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. The first author (KHK) was partially supported by the BK-21 project and KOSEF(98-0701-03-01-5). The second author (DWL) was partially supported by BK-21 project. The third author (FM) was partially supported by Dirección General de Enseñanza Superior (DGES) of Spain under grant PB96-0120-C03-01. The fourth author (SBP) was partially supported by the Hwarangdae Research Institute. Publicado
- Published
- 2001