Differential orthogonality: Laguerre and Hermite cases with applications

JOURNAL OF APPROXIMATION THEORY

卷:196

Article

Borrego-Morell, J.¹  Pijeira-Cabrera, H.² 

[1] Univ Estadual Paulista, UNESP, IBILCE, Sao Paulo, Brazil

[2] Univ Carlos III Madrid, E-28903 Getafe, Spain

关键词: Orthogonal polynomials;    Ordinary differential operators;    Asymptotic analysis;    Weak star convergence;    Hydrodynamic;   

DOI  :  10.1016/j.jat.2015.03.005

来源: Elsevier

【 摘 要 】

Let mu be a finite positive Borel measure supported on R, L[f] = xf '' + (alpha +1 - x)f' with alpha > -1, or L[f] = 1/2f '' - xf', and m a natural number. We study algebraic, analytic and asymptotic properties of the sequence of monic polynomials {Q(n)}(n>m) that satisfy the orthogonality relations integral L[Q(n)](x)x(k)d mu(x) = 0 for all 0 <= k <= n - 1. We also provide a fluid dynamics model for the zeros of these polynomials. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free