Sobolev orthogonal polynomials relative to $\lambda p(c)q(c) + $

Commun. Korean Math. Soc. 1997 Vol. 12, No. 3, 603-617

I. H. Jung, K. H. Kwon, J. K. Lee KAIST, KAIST, Sunmoon university

Abstract : Consider a Sobolev inner product on the space of polynomials such as $$ \phi(p,q) = \lambda p(c)q(c) + \la \tau , p'(x) q' (x) \ra , $$ where $\tau$ is a moment functional and $c$ and $\lambda$ are real constants. We investigate properties of orthogonal polynomials relative to $\phi(\cdot,\cdot)$ and give necessary and sufficient conditions under which such Sobolev orthogonal polynomials satisfy a spectral type differential equation with polynomial coefficients.

Keywords : Sobolev orthogonal polynomials, spectral type differential equation