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.
Similar content being viewed by others
References
Bourgain J. [1990] Problems of almost everywhere convergence related to harmonic analysis and number theory, Israël J. Math., 71, p. 97–127.
Breiman L. [1992]. Probability, SIAM Ed.
Hardy G.H., Wright E.M. [1979] An introduction to the theory of numbers, Oxford at the Clarendon Press, Fifth ed.
Gál I.S., Koksma J.F. [1950] Sur l’ordre de grandeur des fonctions sommables, Indag. Math. 12 p.192–207.
Marczinkiewicz J., Salem R. [1940] Sur les sommes riemanniennes, Comp. Math., 7, p. 376–389.
Rudin W., An arithmetic property of Riemann sums, Proc. Amer. Math. Soc., 15, 1964, p. 321–324.
Spitzer F.L. [1976] Principles of random walks, Second Edition, Springer, New-York.
Weber M. [2003] An arithmetical property of Rademacher sums, to appear in Indagationes Math.
Weber M. [2003] Uniform bounds under increments conditions, submitted.
Author information
Authors and Affiliations
Corresponding author
Rights 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
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03323005