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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
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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

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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 Unpublished.Google Scholar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