Please use this identifier to cite or link to this item: http://hdl.handle.net/10016/6561

 Google™ Scholar. Others By: Díaz Mendoza, Carlos J. - Orive, Rafael - Pijeira, Héctor
Files in This Item:
 zeros_pijeira_jcam_2009_ps.pdf postprint version 182,19 kB Adobe PDF
 Title: Zeros and logarithmic asymptotics of Sobolev orthogonal polynomials for exponential weights Author(s): Díaz Mendoza, Carlos J.Orive, RafaelPijeira, Héctor Publisher: Elsevier Issued date: 1-Dec-2009 Citation: Journal of Computational and Applied Mathematics, 2009, vol. 233, n. 3, p. 691-698 URI: http://hdl.handle.net/10016/6561 ISSN: 0377-0427 DOI: 10.1016/j.cam.2009.02.037 Description: 8 pages, no figures.-- MSC2000 code: 42C05.Zbl#: Zbl 1177.42020 Abstract: We obtain the (contracted) weak zero asymptotics for orthogonal polynomials with respect to Sobolev inner products with exponential weights in the real semiaxis, of the form $x\sp \gamma e\sp {\-varphi(x)}$ with γ>0, which include as particular cases the counterparts of the so-called Freud (i.e., when φ has a polynomial growth at infinity) and Erdös (when φ grows faster than any polynomial at infinity) weights. In addition, the boundness of the distance of the zeros of these Sobolev orthogonal polynomials to the convex hull of the support and, as a consequence, a result on logarithmic asymptotics are derived. Sponsor: The research of C.D.M. and R.O. was partially supported by Dirección General de Investigación, Ministerio de Ciencia y Tecnología of Spain, under grants MTM2005-08571 and MTM2007-68114. The research of H.P. was partially supported by Dirección General de Investigación, Ministerio de Ciencia y Tecnología of Spain, under grant MTM2006-13000-C03-02, by Comunidad de Madrid- Universidad Carlos III de Madrid, under grant CCG06-UC3M/EST-0690 and by Centro de Investigación Matemática de Canarias (CIMAC). Review: PeerReviewed Publisher version: http://dx.doi.org/10.1016/j.cam.2009.02.037 Keywords: Logarithmic potential theorySobolev orthogonal polynomialsZero locationAsymptotic behaviorExponential weights Rights: © Elsevier Appears in Collections: DM - GAMA - Artículos de Revistas