Perturbations on the antidiagonals of Hankel matrices

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 su...

Full description

Saved in:
Bibliographic Details
Published in:Applied mathematics and computation 2013-09, Vol.221, p.444-452
Main Authors: Castillo, K., Dimitrov, D.K., Garza, L.E., Rafaeli, F.R.
Format: Article
Language:English
Subjects:
Asymptotic properties
Hankel matrices
Hankel matrix
Invariance
Laguerre-Hahn class
Linear moment functional
Mathematical models
Orthogonal polynomials
Perturbation methods
Polynomials
Preserves
Transformations
Zeros
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2013.07.004