Random Menshov spectra

Kozma, Gady; Olevskiǐ, Alexander

doi:10.1090/S0002-9939-03-06879-5

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Random Menshov spectra

Authors: Gady Kozma and Alexander Olevskii
Journal: Proc. Amer. Math. Soc. 131 (2003), 1901-1906
MSC (2000): Primary 42A63, 42A61, 42A55
Published electronically: January 8, 2003
MathSciNet review: 1955279
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that the spectra $\Lambda$ of frequencies $\lambda$ obtained by random perturbations of the integers allows one to represent any measurable function on $\mathbb{R}$ by an almost everywhere converging sum of harmonics:

$\begin{displaymath}f=\sum _{\Lambda}c_{\lambda}e^{i\lambda t}.\end{displaymath}$

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4. Gady Kozma and Alexander Olevskiĭ, Representation of non-periodic functions by trigonometric series with almost integer frequencies, C. R. Acad. Sci. Paris Sér. I Math. 329 (1999), no. 4, 275–280 (English, with English and French summaries). MR 1713331 (2000e:42001), http://dx.doi.org/10.1016/S0764-4442(00)88566-3
5. Gady Kozma and Alexander Olevskiĭ, Menshov representation spectra, J. Anal. Math. 84 (2001), 361–393. MR 1849207 (2002h:42024), http://dx.doi.org/10.1007/BF02788115

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Additional Information

Gady Kozma
Affiliation: The Weizmann Institute of Science, Rehovot, Israel
Email: gadykozma@hotmail.com, gadyk@wisdom.weizmann.ac.il

Alexander Olevskii
Affiliation: School of Mathematical Sciences, Tel Aviv University, Ramat-Aviv, Israel 69978
Email: olevskii@math.tau.ac.il

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06879-5
PII: S 0002-9939(03)06879-5
Keywords: Random spectra, representation of functions by trigonometric series
Received by editor(s): February 8, 2002
Published electronically: January 8, 2003
Additional Notes: Research supported in part by the Israel Science Foundation
Communicated by: Andreas Seeger
Article copyright: © Copyright 2003 American Mathematical Society