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- Perturbations on the antidiagonals of Hankel matrices
- Universidade Estadual Paulista (UNESP)
- Universidad de Colima
- 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.
- Applied Mathematics and Computation, v. 221, p. 444-452.
- Hankel matrix
- Laguerre-Hahn class
- Linear moment functional
- Orthogonal polynomials
- Linear moments
- Orthogonal polynomial
- Linear transformations
- Matrix algebra
- Orthogonal functions
- Mathematical transformations
- Acesso restrito
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