Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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SOBOLEV ORTHOGONAL POLYNOMIALS RELATIVE TO ${\lambda}$p(c)q(c) + <${\tau}$,p'(x)q'(x)>

  • Jung, I.H. (Department of Mathematics, KAIS) ;
  • Kwon, K.H. (Department of Mathematics, KAIST) ;
  • Lee, J.K. (Department of Mathematics, Sunmoon University)
  • Published : 1997.07.01
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Abstract

Consider a Sobolev inner product on the space of polynomials such as $$ \phi(p,q) = \lambda p(c)q(c) + <\tau,p'(x)q'(x)> $$ 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

References

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