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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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: We show that the spectra $\Lambda$ of frequencies $\lambda$ obtained by random perturbations of the integers allows one to represent any measurable function $f$ 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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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