Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ORTHOGONAL POLYNOMIALS RELATIVE TO LINEAR PERTURBATIONS OF QUASI-DEFINITE MOMENT FUNCTIONALS

  • Kwon, K.H. (Department of Mathematics, KAIST) ;
  • Lee, D.W. (Department of Mathematics, KAIST) ;
  • Lee, J.H. (Kyungpook National University)
  • Published : 1999.08.01
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Abstract

Consider a symmetric bilinear form defined on $\prod\times\prod$ by $_{\lambda\mu}$ = $<\sigma,fg>\;+\;\lambdaL[f](a)L[g](a)\;+\;\muM[f](b)m[g](b)$ ,where $\sigma$ is a quasi-definite moment functional, L and M are linear operators on $\prod$, the space of all real polynomials and a,b,$\lambda$ , and $\mu$ are real constants. We find a necessary and sufficient condition for the above bilinear form to be quasi-definite and study various properties of corresponding orthogonal polynomials. This unifies many previous works which treated cases when both L and M are differential or difference operators. finally, infinite order operator equations having such orthogonal polynomials as eigenfunctions are given when $\mu$=0.

Keywords

References

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