Monotonicity of zeros of Laguerre-Sobolev-type orthogonal polynomials

Autor(es)

Dimitrov, Dimitar K. ^[1] ; Marcellan, Francisco ^[2] ; Rafaeli, Fernando R. ^[3]

Afiliação do(s) autor(es)

^[1] Univ Estadual Paulista, IBILCE, Dept Ciencias Comp & Estatist, Sao Paulo - Brazil

^[2] Univ Carlos III, Escuela Politecn Super, Dept Matemat, Leganes - Spain

^[3] Univ Estadual Campinas, Inst Matemat Estatist & Comp, BR-13081970 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Mathematical Analysis and Applications; v. 368, n. 1, p. 80-89, AUG 1 2010.
• Citações Web of Science: 13

Resumo

Denote by x(n,k)(M,N)(alpha), k = 1, ..., n, the zeros of the Laguerre-Sobolev-type polynomials L(n)((alpha, M, N))(x) orthogonal with respect to the inner product < p, q > = 1/Gamma(alpha + 1) integral(infinity)(0)p(x)q(x)x(alpha)e(-x) dx + Mp(0)q(0) + Np'(0)q'(0), where alpha > -1, M >= 0 and N >= 0. We prove that x(n,k)(M,N)(alpha) interlace with the zeros of Laguerre orthogonal polynomials L(n)((alpha))(x) and establish monotonicity with respect to the parameters M and N of x(n,k)(M,0)(alpha) and x(n,k)(0,N)(alpha). Moreover, we find N(0) such that x(n,n)(M,N)(alpha) < 0 for all N > N(0), where x(n,n)(M,N)(alpha) is the smallest zero of L(n)((alpha, M, N))(x). Further, we present monotonicity and asymptotic relations of certain functions involving x(n,k)(M,0)(alpha) and x(n,k)(0,N)(alpha). (C) 2010 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 03/01874-2 - Polinômios ortogonais e similares: propriedades e aplicações
• Beneficiário: Alagacone Sri Ranga
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 07/02854-6 - Zeros de polinômios ortogonais e de funções especiais
• Beneficiário: Fernando Rodrigo Rafaeli
• Modalidade de apoio: Bolsas no Brasil - Doutorado