Asymptotic properties of Fourier transforms of \(b\)-decomposable distributions
The author summarizes the content of this paper in the following abstract of this paper: ``Erdös-Kahane numbers (EK numbers) are introduced in relation to the decay of the Fourier transforms of non-symmetric Bernoulli convolutions. The PV, PS, and EK numbers are characterized by using a certain trigonometric series \(H_b(u)\). The relations between those numbers and the asymptotic properties of the Fourier transforms of full \(b\)-decomposable distributions are shown. A sufficient condition for the absolute continuity of one-dimensional \(b\)-decomposable distributions is given. As an application, an open problem on the uniform decay of the Fourier transforms of refinable distributions, raised by \textit{X.-R. Dai, D.-J. Feng} and \textit{Y. Wang} [J. Funct. Anal. 250, No. 1, 1--20 (2007; Zbl 1128.42018)], is solved. Finally, temporal evolution on continuity properties of distributions of some Lévy processes is discussed.''
scientific article; zbMATH DE number 6112965
scientific article