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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

MONOTONICITY AND ASYMPTOTICS OF ZEROS OF LAGUERRE-SOBOLEV-TYPE ORTHOGONAL POLYNOMIALS OF HIGHER ORDER DERIVATIVES

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Author(s):
Marcellan, Francisco [1] ; Rafaeli, Fernando R. [2]
Total Authors: 2
Affiliation:
[1] Univ Carlos III Madrid, Dept Matemat, Escuela Politecn Super, Leganes 28911 - Spain
[2] Univ Estadual Campinas, Inst Matemat Estat & Comp Cient, Sao Paulo - Brazil
Total Affiliations: 2
Document type: Journal article
Source: Proceedings of the American Mathematical Society; v. 139, n. 11, p. 3929-3936, NOV 2011.
Web of Science Citations: 6
Abstract

In this paper we analyze the location of the zeros of polynomials orthogonal with respect to the inner product (0.1) < p,q > = integral(infinity)(0) p(x)q(s)x(alpha)e(-x)dx + Np((j))(0)q((j))(0), where alpha > -1, N >= 0, and j is an element of N. In particular, we focus our attention on their interlacing properties with respect to the zeros of Laguerre polynomials as well as on the monotonicity of each individual zero in terms of the mass N. Finally, we give necessary and sufficient conditions in terms of N in order for the least zero of any Laguerre-Sobolev-type orthogonal polynomial to be negative. (AU)