Random Menshov spectra

Kozma, Gady; Olevskiǐ, Alexander

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

Random Menshov spectra
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by Gady Kozma and Alexander Olevskiǐ PDF

Proc. Amer. Math. Soc. 131 (2003), 1901-1906 Request permission

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: \[ f=\sum _{\Lambda }c_{\lambda }e^{i\lambda t}.\]

References

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