Perturbations on the antidiagonals of Hankel matrices - Castillo, K. [UNESP]; Dimitrov, D. K. [UNESP]; Garza, L. E.; Rafaeli, F. R. [UNESP] (Elsevier, 2013)
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. © 2013 Elsevier Ltd. All rights reserved.
Keywords: Hankel matrix; Laguerre-Hahn class; Linear moment functional; Orthogonal polynomials; Zeros; Linear moments; Orthogonal polynomial; Linear transformations; Matrix algebra; Orthogonal functions; Mathematical transformations