TY - JOUR
AU - Saulius Norvidas
PY - 2017/05/10
Y2 - 2022/09/27
TI - On a uniqueness theorem for characteristic functions
JF - Nonlinear Analysis: Modelling and Control
JA - NAMC
VL - 22
IS - 3
SE - Articles
DO - 10.15388/NA.2017.3.9
UR - https://www.journals.vu.lt/nonlinear-analysis/article/view/13395
AB - 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.
ER -