An observation on the Turán–Nazarov inequality

Volume 218 / 2013

Omer Friedland, Yosef Yomdin Studia Mathematica 218 (2013), 27-39 MSC: Primary 26D05; Secondary 30E05, 42A05. DOI: 10.4064/sm218-1-2


The main observation of this note is that the Lebesgue measure $\mu $ in the Turán–Nazarov inequality for exponential polynomials can be replaced with a certain geometric invariant $\omega \ge \mu $, which can be effectively estimated in terms of the metric entropy of a set, and may be nonzero for discrete and even finite sets. While the frequencies (the imaginary parts of the exponents) do not enter the original Turán–Nazarov inequality, they necessarily enter the definition of $\omega $.


  • Omer FriedlandInstitut de Mathématiques de Jussieu
    Université Pierre et Marie Curie (Paris 6)
    4 Place Jussieu
    75005 Paris, France
  • Yosef YomdinDepartment of Mathematics
    The Weizmann Institute of Science
    Rehovot 76100, Israel

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