Determination of all coherent pairs of functionals
نویسنده
چکیده
A pair of quasi-de nite linear functionals fu0; u1g on the set of polynomials is called a coherent pair if their corresponding sequences of monic orthogonal polynomials fPng and fTng satisfy a relation Tn = P 0 n+1 n+ 1 nP 0 n n ; n 1; with n non-zero constants. We prove that if fu0; u1g is a coherent pair, then at least one of the functionals has to be classical, i.e. Hermite, Laguerre, Jacobi or Bessel. A similar result is derived for symmetrically coherent pairs. AMS Subject Classi cation (1991): 33C45.
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