Skip to main content
Log in

A Theorem related to Marcinkiewicz-Salem Conjecture

  • Published:
Results in Mathematics Aims and scope Submit manuscript

Abstract

Let Sn, n = 1,2… be the sequence of partial sums of independent Bernoulli random variables. We show, for the randomly sampled trigonometric system {eSℓ,ℓ in N}, the validity of the Marcinkiewicz-Salem Conjecture.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bourgain J. [1990] Problems of almost everywhere convergence related to harmonic analysis and number theory, Israël J. Math., 71, p. 97–127.

    Article  MathSciNet  MATH  Google Scholar 

  2. Breiman L. [1992]. Probability, SIAM Ed.

  3. Hardy G.H., Wright E.M. [1979] An introduction to the theory of numbers, Oxford at the Clarendon Press, Fifth ed.

    MATH  Google Scholar 

  4. Gál I.S., Koksma J.F. [1950] Sur l’ordre de grandeur des fonctions sommables, Indag. Math. 12 p.192–207.

    Google Scholar 

  5. Marczinkiewicz J., Salem R. [1940] Sur les sommes riemanniennes, Comp. Math., 7, p. 376–389.

    Google Scholar 

  6. Rudin W., An arithmetic property of Riemann sums, Proc. Amer. Math. Soc., 15, 1964, p. 321–324.

    Article  MathSciNet  MATH  Google Scholar 

  7. Spitzer F.L. [1976] Principles of random walks, Second Edition, Springer, New-York.

    Book  Google Scholar 

  8. Weber M. [2003] An arithmetical property of Rademacher sums, to appear in Indagationes Math.

  9. Weber M. [2003] Uniform bounds under increments conditions, submitted.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Michel Weber.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Weber, M. A Theorem related to Marcinkiewicz-Salem Conjecture. Results. Math. 45, 169–184 (2004). https://doi.org/10.1007/BF03323005

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03323005

2000 Mathematical Subject Classification

Keywords

Navigation