Abstract
The spaces χp,α induce a classification of the closed subsets Θ ofT, the reals modulo 1, as sets of (p,α) multiplicity (or (p, α uniqueness) as Θ is (or is not) the support of a non-zero distribdtion ψ such that ψ4 (n) ∈ χp,α.
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A. Devinatz and I. I. Hirschman, Jr.,Multiplier transformations on l 2,α Ann. of Math.69 (1959), 575–587.
J. P. Kahane and R. Salem,Ensembles parfaits et séries trigonométriques, Paris (1963).
I. Katznelson,Sets of uniqueness for some classes of trigonometrical series, Bull. Amer. Math. Soc.70 (1964), 722–723.
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Research supported in part by the United States Air Force Office of Scientific Research under contract No. AF-AFOSR 721-65.
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Hirschman, I.I., Katznelson, Y. Sets of uniqueness and multiplicity forl p,α . Israel J. Math. 3, 221–231 (1965). https://doi.org/10.1007/BF03008400
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DOI: https://doi.org/10.1007/BF03008400