Continuous symmetric Sobolev inner products

24 pages, no figures.-- MSC2000 codes: 42C05.MR#: MR1953647 (2003j:42029)Zbl#: Zbl pre05368623In this paper we consider the sequence of monic polynomials (Qn) orthogonal with respect to a symmetric Sobolev inner product. If Q_2n(x)=Pn(x^2) and Q_2n+1(x)=xRn(x^2), then we deduce the integral representation of the inner products such that (Pn) and (Rn) are, respectively, the corresponding sequences of monic orthogonal polynomials. In the semiclassical case, algebraic relations between such sequences are deduced. Finally, an application of the above results to Freud-Sobolev polynomials is given.The work of the second author was partially supported by Dirección General de Investigación (Ministerio de Ciencia y Tecnología) of Spain under grant BFM 2000-0206-C04-01 and INTAS project INTAS 2000-272.Publicad