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Littlewood–Paley theorems for sum and difference sets

Published online by Cambridge University Press:  24 October 2008

Garth I. Gaudry
Garth I. Gaudry
Affiliation:
Flinders University of South Australia
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Summary

Let α be a positive integer, and El, …, Eα Hadamard sets of positive integers. It is shown that E = E1 + … + Eα determines a Littlewood–Paley decomposition of Z.

Suppose that is a Hadamard set of positive integers such that nj+1/nj ≥ 2 for all j. Let α be a positive integer, and

We show that F(α) also determines a Littlewood-Paley decomposition of Z.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 83 , Issue 1 , January 1978 , pp. 65 - 71
Copyright
Copyright © Cambridge Philosophical Society 1978

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References

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