Vol. 69, No. 2, 1977

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Unimodality of the Lévy spectral function

Carol Alf and Thomas Alfonso O’Connor

Vol. 69 (1977), No. 2, 285–290
Abstract

A. Ya. Khinchin proved that if Φ and Ψ are characteristic functions and Φ(t) = t1 0tΨ(u)du, then the distribution function of Φ is convex on (−∞,0) and concave on (0,+). A similar theorem is proved here for logarithms of infinitely divisible characteristic functions and their Lévy spectral functions.

Mathematical Subject Classification 2000
Primary: 60E05
Milestones
Received: 20 April 1976
Revised: 11 October 1976
Published: 1 April 1977
Authors
Carol Alf
Thomas Alfonso O’Connor