Asymptotic properties of Fourier transforms of \(b\)-decomposable distributions
type: Item
instance of: scholarly article
title: Asymptotic properties of Fourier transforms of \(b\)-decomposable distributions
zbMATH Open document ID: 1257.42018
author: Toshiro Watanabe
published in: The Journal of Fourier Analysis and Applications
publication date: 2012-12-06T00:00:00Z
review text: 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.''
reviewed by: Kun Soo Chang
Mathematics Subject Classification ID: 42B10
Mathematics Subject Classification ID: 60G30
zbMATH DE Number: 6112965
zbMATH Keywords: \(b\)-decomposable distribution
zbMATH Keywords: EK number
zbMATH Keywords: Bernoulli convolution
zbMATH Keywords: Lévy process
MaRDI profile type: Publication
full work available at URL: s00041-012-9222-9
OpenAlex ID: W1988617276
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DOI: 10.1007/S00041-012-9222-9
description: scientific article; zbMATH DE number 6112965