A non-standard class of sobolev orthogonal polynomials

  • Han, S.S. (Department of Liberal Arts, Myongji University, Yongin 449-728, Korea, E-mail : hahn@wh.myongji.ac.kr) ;
  • Jung, I.H. (Department of Mathematics, KAIST, Taejon 305-701) ;
  • Kwon, K.H. (Department of Mathematics, KAIST, Taejon 305-701, Korea, E-mail : khkwon@jacobi.kaist.ac.kr) ;
  • Lee, J.K.. (Department of Mathematics, Sunmoon university)
  • Published : 1997.10.01

Abstract

When $\tau$ is a quasi-definite moment functional on P, the vector space of all real polynomials, we consider a symmetric bilinear form $\phi(\cdot,\cdot)$ on $P \times P$ defined by $$ \phi(p,q) = \lambad p(a)q(a) + \mu p(b)q(b) + <\tau,p'q'>, $$ where $\lambda,\mu,a$, and b are real numbers. We first find a necessary and sufficient condition for $\phi(\cdot,\cdot)$ and show that such orthogonal polynomials satisfy a fifth order differential equation with polynomial coefficients.

Keywords

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