Random Menshov spectra
Authors:
Gady Kozma and Alexander Olevskii
Journal:
Proc. Amer. Math. Soc. 131 (2003), 1901-1906
MSC (2000):
Primary 42A63, 42A61, 42A55
DOI:
https://doi.org/10.1090/S0002-9939-03-06879-5
Published electronically:
January 8, 2003
MathSciNet review:
1955279
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Abstract | References | Similar Articles | Additional Information
Abstract: We show that the spectra 
of frequencies 
obtained by random perturbations of the integers allows one to represent any measurable function 
on 
by an almost everywhere converging sum of harmonics:
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- 2. R. S. Davtjan, The representation of measurable functions by Fourier integrals, Akad. Nauk Armjan. SSR Dokl. 53 (1971), 203–207 (Russian, with Armenian summary). MR 0294990
- 3. Alexander Olevskiĭ, Completeness in 𝐿²(𝐑) of almost integer translates, C. R. Acad. Sci. Paris Sér. I Math. 324 (1997), no. 9, 987–991 (English, with English and French summaries). MR 1451238, https://doi.org/10.1016/S0764-4442(97)87873-1
- 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, https://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, https://doi.org/10.1007/BF02788115
, Completeness in 
of almost integer translates, C.R. Acad. Sci. Paris, Sèr. I Math., 324 (1997), 987-991. 
, Representations of non-periodic functions by trigonometric series with almost integer frequencies, C.R. Acad. Sci. Paris, Sèr. I Math., 329 (1999), 275-280. Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 42A63, 42A61, 42A55
Retrieve articles in all journals with MSC (2000): 42A63, 42A61, 42A55
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:
https://doi.org/10.1090/S0002-9939-03-06879-5
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