Littlewood–Paley theorems for sum and difference sets

Littlewood–Paley theorems for sum and difference sets

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) al...

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Veröffentlicht in:Mathematical proceedings of the Cambridge Philosophical Society 1978-01, Vol.83 (1), p.65-71
1. Verfasser: Gaudry, Garth I.
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:0305-0041
1469-8064
DOI:10.1017/S0305004100054293