Perturbations on the subdiagonals of Toeplitz matrices Articles uri icon

publication date

  • March 2011

start page

  • 1563

end page

  • 1579

issue

  • 6

volume

  • 434

international standard serial number (ISSN)

  • 0024-3795

electronic international standard serial number (EISSN)

  • 1873-1856

abstract

  • Let L be an Hermitian linear functional defined on the linear space of Laurent polynomials. It is very well known that the Gram matrix of the associated bilinear functional in the linear space of polynomials is a Toeplitz matrix. In this contribution we analyze some linear spectral transforms of L such that the corresponding Toeplitz matrix is the result of the addition of a constant in a subdiagonal of the initial Toeplitz matrix. We focus our attention in the analysis of the quasi-definite character of the perturbed linear functional as well as in the explicit expressions of the new monic orthogonal polynomial sequence in terms of the first one.