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Perturbations of Laguerre–Hahn linear functionals

✍ Scribed by F. Marcellán; E. Prianes

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
147 KB
Volume
105
Category
Article
ISSN
0377-0427

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✦ Synopsis

In this paper we shall make some perturbations in a Laguerre-Hahn linear functional, such as the addition of a Dirac Delta or the left multiplication by a polynomial. We shall study that these transformations carried out on Laguerre-Hahn linear functionals originate new Laguerre-Hahn linear functionals. We shall also analyze the class of the resulting functional.

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Let u be a Hermitian linear functional defined in the linear space of Laurent polynomials and F its corresponding Carathéodory function. We establish the equivalence between a Riccati differential equation with polynomial coefficients for F , zAF = BF 2 + CF + D, and a distributional equation for u,