Characteristic functions of polynomial-normal distributions

The densities of polynomial-normal distributions (PND) are the product of nonegative polynomials and normal densities. These densities provide a rich class of distributions that can be used in modeling when faced with nonnormal characteristics such as skewness and multimodality. We give necessary and sufficient conditions for φ to be a characteristic function (ch.f.) of a PND. Then we given an effective construction of the ch.f. of a PND. Proceedings of the Seminar on Stability Problems for Stochastic Models, Vologda, Russia, 1998, Part I.