Israel Journal of Mathematics

, Volume 3, Issue 4, pp 221–231 | Cite as

Sets of uniqueness and multiplicity forl p,α

  • I. I. Hirschman
  • Y. Katznelson


The spaces χ p,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) ∈ χ p,α .


Positive Integer Closed Subset Positive Measure Trigonometric Polynomial Trigonometrical Series 
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  1. 1.
    A. Devinatz and I. I. Hirschman, Jr.,Multiplier transformations on l 2,α Ann. of Math.69 (1959), 575–587.CrossRefMathSciNetGoogle Scholar
  2. 2.
    J. P. Kahane and R. Salem,Ensembles parfaits et séries trigonométriques, Paris (1963).Google Scholar
  3. 3.
    I. Katznelson,Sets of uniqueness for some classes of trigonometrical series, Bull. Amer. Math. Soc.70 (1964), 722–723.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Hebrew University 1965

Authors and Affiliations

  • I. I. Hirschman
    • 1
  • Y. Katznelson
    • 1
  1. 1.Stanford UniversityStanford

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