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

Autor(es)

Marcellan, Francisco ^[1] ; Rafaeli, Fernando R. ^[2]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: Proceedings of the American Mathematical Society; v. 139, n. 11, p. 3929-3936, NOV 2011.
• Citações Web of Science: 6

Resumo

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)

• Processo FAPESP: 07/02854-6 - Zeros de polinômios ortogonais e de funções especiais
• Beneficiário: Fernando Rodrigo Rafaeli
• Modalidade de apoio: Bolsas no Brasil - Doutorado