@article{Norvidas_2017, title={On a uniqueness theorem for characteristic functions}, volume={22}, url={https://www.journals.vu.lt/nonlinear-analysis/article/view/13395}, DOI={10.15388/NA.2017.3.9}, abstractNote={<p>Suppose that <em>f</em> is the characteristic function of a probability measure on the real line <em>R</em>. We deal with the following open problem posed by N.G. Ushakov: Is it true that <em>f</em> is never determined by its imaginary part Im <em>f</em>? In other words, is it true that for any characteristic function <em>f</em>, there exists a characteristic function <em>g</em> such that Im <em>f</em> = Im <em>g</em>, but <em>f</em> ≠ <em>g</em>? 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.</p>}, number={3}, journal={Nonlinear Analysis: Modelling and Control}, author={Norvidas, Saulius}, year={2017}, month={May}, pages={412-420} }