Stability bounds of decompositions of infinitely divisible distribution functions with Gaussian component of linnik's class $$\mathfrak{L}$$

Abstract

Linnik introduced the class ~ of distribution functions (d.f.s) (see [i, p. 129]) in connection with the description of necessary conditions of membership of a d.f. with a Gaussian component in the class |0 The class |0 consists of infinitely divisible d.f.s that have only infinitely divisible components. Linnik proved that if a d.f. with a Gaussian component belongs to the class ]0 , then it belongs to the class ~ , i.e., its characteristic function (c.f.) has the form