Perturbations on the antidiagonals of Hankel matrices

K. Castillo, D. K. Dimitrov, L. E. Garza*, F. R. Rafaeli

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)444-452
Number of pages9
JournalApplied Mathematics and Computation
Publication statusPublished - 2013
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics


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