Additive spectra of the 1/4 Cantor measure

In this paper, we add to the characterization of the Fourier spectra for Bernoulli convolution measures. These measures are supported on Cantor subsets of the line. We prove that performing an odd additive translation to half the canonical spectrum for the 1/4 Cantor measure always yields an alterna...

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Bibliographic Details
Published in:arXiv.org 2013-10
Main Authors: Jorgensen, Palle E T, Kornelson, Keri A, Shuman, Karen L
Format: Article
Language:English
Subjects:
Convolution
Online Access:Get full text
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Summary:In this paper, we add to the characterization of the Fourier spectra for Bernoulli convolution measures. These measures are supported on Cantor subsets of the line. We prove that performing an odd additive translation to half the canonical spectrum for the 1/4 Cantor measure always yields an alternate spectrum. We call this set an additive spectrum. The proof works by connecting the additive set to a spectrum formed by odd multiplicative scaling.
ISSN:2331-8422