Published online by Cambridge University Press: 24 October 2008
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.