Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Journals Home Search My Subscriptions Subscribe
Previous issue | This issue | Most recent issue | All issues (1950–Present) | Next issue | Previous article | Articles in press | Recently published articles | Next article
Request Permissions
 
 

 

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
Full-text PDF

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 $f$ on $\mathbb{R} $ by an almost everywhere converging sum of harmonics:

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

References [Enhancements On Off] (What's this?)

  • 1. N. Bary, A Treatise on Trigonometric Series, vol. II, Pergamon Press Inc., NY (1964). MR 30:1347
  • 2. R.S. Davtjan, The representation of measurable functions by Fourier integrals, Akad. Nauk. Armjan. SSR Dokl. 53 (1971), 203-207. (Russian, Armenian abstract) MR 45:4058
  • 3. A. Olevski{\v{\i}}\kern.15em, Completeness in $L^{2}(\mathbf{R})$ of almost integer translates, C.R. Acad. Sci. Paris, Sèr. I Math., 324 (1997), 987-991. MR 98a:42002
  • 4. G. Kozma and A. Olevski{\v{\i}}\kern.15em, Representations of non-periodic functions by trigonometric series with almost integer frequencies, C.R. Acad. Sci. Paris, Sèr. I Math., 329 (1999), 275-280. MR 2000e:42001
  • 5. G. Kozma and A. Olevskii, Menshov Representation Spectra, Journal d'Analyse Mathématique, 84 (2001), 361-393. MR 2002h:42024

Similar Articles

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

American Mathematical Society