an:01546733
Zbl 0980.42018
Alfaro, Manuel; Rezola, M. Luisa; P??rez, Teresa E.; Pi??ar, Miguel A.
On symmetric differential operators associated with Sobolev orthogonal polynomials: A characterization
EN
Acta Appl. Math. 61, No. 1-3, 3-14 (2000).
00069597
2000
j
42C05 33C45
Sobolev orthogonal polynomials; classical orthogonal polynomials; Sobolev bilinear form; second order differential operator
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''.
Andrei Mart??nez Finkelshtein (Almeria)