Vol. 29, No. 3, 1969

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On the decomposition of infinitely divisible characteristic functions with continuous Poisson spectrum. II

Roger Cuppens

Vol. 29 (1969), No. 3, 521–525

Let f be an infinitely divisible characteristic function whose spectral functions are absolutely continuous functions with almost everywhere continuous derivatives. Some necessary conditions that f belong to the class I0 of the infinitely divisible characteristic functions without indecomposable factors have been obtained by Cramér, Shimizu and the author and a sufficient condition that f belong to I0 has been given by Ostrovskiy. In the present work, we prove that the condition of Ostrovskiy is not only a sufficient, but also a necessary condition that f belong to I0.

Mathematical Subject Classification
Primary: 60.20
Received: 27 May 1968
Published: 1 June 1969
Roger Cuppens