Stimulated by a problem of Kruglov and a result of Titov we derive an elementary continuation theorem for distribution functions. It implies the following generalization of Carmér’s theorem. Let and be two non-degenerate distribution functions such that
where and stands for the normal distribution ; if the corresponding characteristic functions and do not vanish in the upper half plane, then and are also normal. Linnik’s theorem can be analogously generalized. More general variants are also discussed.
Cite this article
H.-J. Rossberg, Generalization of Cramér’s and Linnik’s Factorization Theorems in the Continuation Theory of Distribution Functions. Z. Anal. Anwend. 4 (1985), no. 3, pp. 193–200