Perturbations on the antidiagonals of Hankel matrices
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Data
2013-08-12
Autores
Castillo, K. [UNESP]
Dimitrov, D. K. [UNESP]
Garza, L. E.
Rafaeli, F. R. [UNESP]
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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. © 2013 Elsevier Ltd. All rights reserved.
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Hankel matrix, Laguerre-Hahn class, Linear moment functional, Orthogonal polynomials, Zeros, Linear moments, Orthogonal polynomial, Linear transformations, Matrix algebra, Orthogonal functions, Mathematical transformations
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Applied Mathematics and Computation, v. 221, p. 444-452.