Second kind functionals for the Laguerre-Hahn affine class on the unit circle (Q1420707)

The authors begin with the definition and some properties of the Laguerre-Hahn affine functionals on the unit circle, i.e., Hermitian quasi-definite linear functionals such that their Stieltjes transform satisfies certain linear first order differential equation with polynomial coefficients. They study the second degree functionals and prove that Laguerre-Hahn affine functionals that are not rational and satisfy the Riccati equation must be the second degree functionals. The authors show that for the Laguerre-Hahn affine functionals which are neither second degree nor rational and satisfy an additional condition, the associated second kind functionals do not belong to the Laguerre-Hahn affine class.