Cachafeiro, AliciaMarcellán Español, Francisco JoséMoreno Balcázar, Juan José2009-12-072009-12-072003-11Journal of Approximation Theory, 2004, vol. 125, n. 1, p. 26-410021-9045https://hdl.handle.net/10016/597716 pages, no figures.-- MSC2000 codes: 33C45; 33C47; 42C05.MR#: MR2016838 (2005e:33004)Zbl#: Zbl 1043.33005In this paper we consider a Sobolev inner product $(f,g)_S=\int fg\,d\mu+ \lambda \int f'g'\,d\mu (*)$, and we characterize the measures μ for which there exists an algebraic relation between the polynomials, {Pn}, orthogonal with respect to the measure μ and the polynomials, {Qn}, orthogonal with respect to (*), such that the number of involved terms does not depend on the degree of the polynomials. Thus, we reach in a natural way the measures associated with a Freud weight. In particular, we study the case $d\mu=e^{-x^4}dx$ supported on the full real axis and we analyze the connection between the so-called Nevai polynomials (associated with the Freud weight $e^{-x^4}$)and the Sobolev orthogonal polynomials Qn. Finally, we obtain some asymptotics for {Qn}.application/pdfeng© ElsevierSobolev orthogonal polynomialsFreud polynomialsAsymptoticsresearch articleMatemáticas10.1016/j.jat.2003.09.003open access