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The Distribution of Sequences Modulo 1

Published online by Cambridge University Press:  20 November 2018

Alan Zame
Alan Zame*
Affiliation:
University of Miami, Coral Gables, Florida
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In a recent paper (2), Helson and Kahane consider the problem of the existence of real numbers x such that the sequence (λn x) (when reduced modulo 1) is not summable by a given regular Toeplitz method, where (λn) is a lacunary sequence of positive real numbers. Thus, as an example, they show the existence of uncountably many x such that the sequence (θn x) does not have a distribution function modulo 1, where θ is some fixed number > 1.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 697 - 709
Copyright
Copyright © Canadian Mathematical Society 1967

References

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