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On symmetric differential operators associated with Sobolev orthogonal polynomials: A characterization. (English) Zbl 0980.42018
Authors’ abstract: “Given the Sobolev bilinear form \[ (f,g)_S=\langle u_0, fg\rangle + \langle u_1, f'g'\rangle , \] with \(u_0\) and \(u_1\) linear functionals, a characterization of the linear second-order differential operators with polynomial coefficients, symmetric with respect to \(( \cdot , \cdot)_S\) in terms of \(u_0\) and \(u_1\) is obtained. In particular, several interesting functionals \(u_0\) and \(u_1\) are considered, recovering as particular cases of our study, results already known in the literature”.
MSC:
42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
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