Perturbations on the antidiagonals of Hankel matrices

Given a strongly regular Hankel matrix, and its associated sequence of moments whichdefines a quasi-definite moment linear functional, we study the perturbation of a fixedmoment, i.e., a perturbation of one antidiagonal of the Hankel matrix. We define a linearfunctional whose action results in such a perturbation and establish necessary and sufficientconditions in order to preserve the quasi-definite character. A relation between thecorresponding sequences of orthogonal polynomials is obtained, as well as the asymptoticbehavior of their zeros. We also study the invariance of the Laguerre-Hahn class of linearfunctionals under such perturbation, and determine its relation with the so-called canonicallinear spectral transformations.The research of the first author was supported by Bolsa de Atração de Jovens Talentos CAPES/CNPq/FAPs of Brazil, Project 370291/2013 1 and Dirección General de Investigación, Ministerio de Economía y Competitividad of Spain, Grant MTM2012 36732 C03 0