Spectral representations of characteristic functions of discrete probability laws (Q2692540)

The authors consider discrete probability laws on the real line with the property that their characteristic function \(f\) are separated from zero \(|f(t)|\ge\mu>0\) for every \(t\). This class includes arbitrary discrete infinitely divisible laws and lattice probability laws having characteristic functions without zeros on the real line. These laws have characteristic functions that admit a spectral Lévy-Khinchine type representation with non-monotonic Lévy spectral measure. These representations are then applied to obtain limit and compactness theorems for convergence in variation