On semiclassical linear functionals: Integral representations (Q1893583)

Integral representations of so-called semiclassical functionals are derived. At first estimates for the moments \(\mu_n\) of two classes of functionals are given. This allows in the first case to define the \(z\)- transform \[ S(z)=- \sum_{n=0}^\infty \mu_n z^{-n-1}, \] which appears to be an analytic function in a neighborhood of infinity. The integral formula for the coefficients \(\mu_n\) leads to an integral representation of the functionals in consideration. The second case is investigated in another manner. Examples are added.