Hostname: page-component-848d4c4894-p2v8j Total loading time: 0 Render date: 2024-06-08T03:37:14.289Z Has data issue: false hasContentIssue false
  • English
  • Français

A Wiener—Wintner property for the helical transform

Published online by Cambridge University Press:  19 September 2008

I. Assani
I. Assani
Affiliation:
Department of Mathematics, The University of North Carolinaat Chapel Hill, CB#3250 Phillips Hall, Chapel Hill, NC 27599-3250, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

Let (X,ℱ,μ,ϕ) be a dynamical system ϕ is an invertible measure-preserving transformation on the measure space (X,ℱ,μ). We show that for each p, 1<p<∞,f ∈ Lp(μ) we can find a single null set off which exists for all ε ℝ.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 12 , Issue 2 , June 1992 , pp. 185 - 194
Copyright
Copyright © Cambridge University Press 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Assani, I.. The Wiener—Wintner property for the helical transform of the shift on [0, l]z. Preprint.Google Scholar
[2]Assani, I.. The helical transform, the a.e. convergence of Fourier series, and a Wiener—Wintner property. Preprint.Google Scholar
[3]Bourgain, J.. Return times of dynamical systems. Unpublished.Google Scholar
[4]Calderón, A.. Ergodic theory and translation-invariant operators. Proc. Nat. Acad. Sci. USA (1968), 349–353.Google Scholar
[5]Campbell, J. & Petersen, K.. The spectral measure and Hilbert transform of a measure preserving transformation. Trans. Amer. Math. Soc. 313 (1989), 121–129.CrossRefGoogle Scholar
[6]Carleson, L.. On convergence and growth of partial sums of Fourier series. Acta Math. 116 (1966), 135–157.Google Scholar
[7]Coquet, J., Kamae, T. & France, M. Mendès. Sur la mesure spectrale de certaines suites arithmétiques. Bull. Soc. Math. France 105 (1977), 369–384.Google Scholar
[8]Cotlar, M.. A unified theory of Hilbert transforms and ergodic theorems. Rev. Mat. Cuyana 1 (1955), 105–167.Google Scholar
[9]Hunt, R.. On the convergence of Fourier series. Orthogonal Expansion and their Continuous Analogues. Haimo, D.T., ed., Carbondale, Southern Illinois University Press, 1968, pp. 235–255.Google Scholar
[10]Jewett, R. I.. The prevalence of uniquely ergodic systems. J. Math. Mech. 19 (1970), 171–729.Google Scholar
[11]Krieger, W.. On unique ergodicity. Proc. Sixth Berekeley Symposium. University of California Press, 1972, pp. 327–346.Google Scholar
[12]Wiener, N. & Wintner, A.. Harmonic analysis and ergodic theory. Amer. J. Math. 63 (1941), 415–426.Google Scholar