Perturbations on the antidiagonals of Hankel matrices

Abstract

abst ractGiven 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 suffi cient 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 canon ical linear spectral transformations.

Robust Stability of Hurwitz Polynomials Associated with Modified Classical Weights

“…Thus, the focus is placed in algebraic and analytic properties of the perturbed polynomials, expressed in terms of the original non-perturbed polynomials. For instance, in [29] the authors consider a perturbation introduced on the coefficients of the recurrence relation, whereas perturbations on the sequence of moments have been considered in [30]. In both cases, an interesting problem is to construct sequences of Hurwitz polynomials by using the approach considered here, and to determine the structure of the obtained uncertainty.…”