Perturbations on the antidiagonals of Hankel matrices Articles uri icon

authors

  • CASTILLO RODRIGUEZ, KENIER
  • DIMITROV, DIMITAR K.
  • GARZA GAONA, LUIS ENRIQUE
  • RAFAELI, FERNANDO R.

publication date

  • September 2013

start page

  • 444

end page

  • 452

volume

  • 221

international standard serial number (ISSN)

  • 0096-3003

electronic international standard serial number (EISSN)

  • 1873-5649

abstract

  • 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.

keywords

  • hankel matrix; linear moment functional; orthogonal polynomials; laguerre-hahn class; zeros