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GENERALIZED Δ-COHERENT PAIRS

  • Kwon, K.H. (Division of Applied Mathematic KAIST) ;
  • Lee, J.H. (Department of Mathematical Science SNU) ;
  • F. Marcellan (Departmento de Matematicas Universidad Carlos III de Madrid Avda)
  • Published : 2004.11.01

Abstract

A pair of quasi-definite linear functionals {u$_{0}$, u$_1$} is a generalized $\Delta$-coherent pair if monic orthogonal polynomials (equation omitted) relative to u$_{0}$ and u$_1$, respectively, satisfy a relation (equation omitted) where $\sigma$$_{n}$ and T$_{n}$ are arbitrary constants and $\Delta$p = p($\chi$+1) - p($\chi$) is the difference operator. We show that if {u$_{0}$, u$_1$} is a generalized $\Delta$-coherent pair, then u$_{0}$ and u$_{1}$ must be discrete-semiclassical linear functionals. We also find conditions under which either u$_{0}$ or u$_1$ is discrete-classical.ete-classical.

Keywords

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