Nonlinear Analysis (May 2017)

On a uniqueness theorem for characteristic functions

  • Saulius Norvidas

DOI
https://doi.org/10.15388/NA.2017.3.9
Journal volume & issue
Vol. 22, no. 3

Abstract

Read online

Suppose that f is the characteristic function of a probability measure on the real line R. We deal with the following open problem posed by N.G. Ushakov: Is it true that f is never determined by its imaginary part Im f? In other words, is it true that for any characteristic function f, there exists a characteristic function g such that Im f = Im g, but f ≠ g? The answer to this question is no. We give a characterization of those characteristic functions, which are uniquely determined by their imaginary parts. Also, several examples of characteristic functions, which are uniquely determined by their imaginary parts, are given.

Keywords