- A non-standard class of sobolev orthogonal polynomials
- Han, S.S. ; Jung, I.H. ; Kwon, K.H. ; Lee, J.K.. ;
- Communications of the Korean Mathematical Society, volume 12, issue 4, 1997, Pages 935~950
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.