Alfaro, Manuel; Rezola, M. Luisa; Pérez, Teresa E.; Piñar, Miguel A. On symmetric differential operators associated with Sobolev orthogonal polynomials: A characterization. (English) Zbl 0980.42018 Acta Appl. Math. 61, No. 1-3, 3-14 (2000). 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”. Reviewer: Andrei Martínez Finkelshtein (Almeria) 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.) Keywords:Sobolev orthogonal polynomials; classical orthogonal polynomials; Sobolev bilinear form; second order differential operator PDFBibTeX XMLCite \textit{M. Alfaro} et al., Acta Appl. Math. 61, No. 1--3, 3--14 (2000; Zbl 0980.42018) Full Text: DOI