Perturbations of Laguerre-Hahn Functional: Modification by the Derivative of a Dirac Delta Articles uri icon

publication date

  • June 2009

start page

  • 59

end page

  • 77

issue

  • 1

volume

  • 20

international standard serial number (ISSN)

  • 1065-2469

electronic international standard serial number (EISSN)

  • 1476-8291

abstract

  • In this paper, we consider a perturbation of a Laguerre-Hahn functional by adding a derivative of a Dirac delta. This transformation leaves invariant the family of Laguerre-Hahn linear functionals. We shall also analyse the class of the perturbed linear functional. Finally, we illustrate these perturbations by adding the derivative of a Dirac delta to the first kind associated functional of the classical Laguerre functional. The expression of the new orthogonal polynomials is obtained.