An observation on the Turán–Nazarov inequality

Omer Friedland ¹   ; Yosef Yomdin ²

¹ Institut de Mathématiques de Jussieu Université Pierre et Marie Curie (Paris 6) 4 Place Jussieu 75005 Paris, France
² Department of Mathematics The Weizmann Institute of Science Rehovot 76100, Israel

Studia Mathematica, Tome 218 (2013) no. 1, pp. 27-39

Résumé

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 $.

Détail

DOI : 10.4064/sm218-1-2

Keywords: main observation note lebesgue measure tur nazarov inequality exponential polynomials replaced certain geometric invariant omega which effectively estimated terms metric entropy set may nonzero discrete even finite sets while frequencies imaginary parts exponents enter original tur nazarov inequality necessarily enter definition nbsp omega