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 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:

- 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
, Completeness in
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
, 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
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