One class of singular complex-valued random variables of the Jessen-Wintner type
We study the structure of the distribution of a complex-valued random variable ξ = Σa k ξ k , where ξ k are independent complex-valued random variables with discrete distribution and a k are terms of an absolutely convergent series. We establish a criterion of discreteness and sufficient conditions for singularity of the distribution of ξ and investigate the fractal properties of the spectrum.
English version (Springer): Ukrainian Mathematical Journal 49 (1997), no. 12, pp 1862-1871.
Citation Example: O. V. Shkol’nyi, Pratsiovytyi M. V. One class of singular complex-valued random variables of the Jessen-Wintner type // Ukr. Mat. Zh. - 1997. - 49, № 12. - pp. 1653–1660.