Zeros and logarithmic asymptotics of Sobolev orthogonal polynomials for exponential weights

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:233

Article; Proceedings Paper

Diaz Mendoza, C.²  Orive, R.²  Pijeira Cabrera, H.¹ 

[1] Univ Carlos III Madrid, Dept Matemat, Leganes 28911, Spain

[2] Univ La Laguna, E-38207 San Cristobal la Laguna, Spain

关键词: Logarithmic potential theory;    Sobolev orthogonal polynomials;    Zero location;    Asymptotic behavior;    Exponential weights;   

DOI  :  10.1016/j.cam.2009.02.037

来源: Elsevier

【 摘 要 】

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(gamma)e(-phi(X)), with gamma > 0, which include as particular cases the counterparts of the so-called Freud (i.e., when phi has a polynomial growth at infinity) and Erdos (when phi 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. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

Free