Additive spectra of the 1/4 Cantor measure

Palle E. T. Jorgensen; Keri A. Kornelson; Karen L. Shuman

Additive spectra of the 1/4 Cantor measure

Spectral Theory 2013-10-29 v1 Functional Analysis

Authors: Palle E. T. Jorgensen , Keri A. Kornelson , Karen L. Shuman

Abstract

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.

Keywords

Fourier spectra Bernoulli convolution measures Cantor measure additive spectrum odd additive translation multiplicative scaling

Cite

@article{arxiv.1310.7242,
  title  = {Additive spectra of the 1/4 Cantor measure},
  author = {Palle E. T. Jorgensen and Keri A. Kornelson and Karen L. Shuman},
  journal= {arXiv preprint arXiv:1310.7242},
  year   = {2013}
}

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9 pages, 1 figure

Additive spectra of the 1/4 Cantor measure

Abstract

Keywords

Cite

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