Perturbations on the antidiagonals of Hankel matrices

Autor(es)

Castillo, K. ^[1] ; Dimitrov, D. K. ^[1] ; Garza, L. E. ^[2] ; Rafaeli, F. R. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Estadual Paulista IBILCE UNESP, Dept Matemat Aplicada, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil

^[2] Univ Colima, Fac Ciencias, Colima - Mexico

• Tipo de documento: Artigo Científico
• Fonte: Applied Mathematics and Computation; v. 221, p. 444-452, SEP 15 2013.
• Citações Web of Science: 3

Resumo

Given a strongly regular Hankel matrix, and its associated sequence of moments which defines a quasi-definite moment linear functional, we study the perturbation of a fixed moment, i.e., a perturbation of one antidiagonal of the Hankel matrix. We define a linear functional whose action results in such a perturbation and establish necessary and sufficient conditions in order to preserve the quasi-definite character. A relation between the corresponding sequences of orthogonal polynomials is obtained, as well as the asymptotic behavior of their zeros. We also study the invariance of the Laguerre-Hahn class of linear functionals under such perturbation, and determine its relation with the so-called canonical linear spectral transformations. (C) 2013 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 09/13832-9 - Polinômios ortogonais, funções especiais e aplicações
• Beneficiário: Dimitar Kolev Dimitrov
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 11/00658-0 - Zeros de polinômios ortogonais
• Beneficiário: Fernando Rodrigo Rafaeli
• Modalidade de apoio: Auxílio à Pesquisa - Jovens Pesquisadores