2011/06/30 by Omer Friedland, Friedland, Omer, Yosef Yomdin +1
Mathematics · #26D05 #30E05 #42A05 #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Mathematical Dynamics and Fractals #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics #math.FA #msc:26D05 #msc:30E05 #msc:42A05
paper · pdf · doi:10.48550/arxiv.1107.0039
openalex publication_date 2011/06/30 · arxiv created 2013/08/07 · arxiv updated 2013/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main observation of this note is that the Lebesgue measure μ in the Turán-Nazarov inequality for exponential polynomials can be replaced with a certain geometric invariant ω≥ μ, 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 in the original Turán-Nazarov inequality, they necessarily enter the definition of ω.