An observation on the Turán-Nazarov inequality

• Autorzy: Omer Friedland , Yosef Yomdin
• Języki publikacji: EN

Abstrakty

EN

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 the original Turán-Nazarov inequality, they necessarily enter the definition of ω.

Kategorie tematyczne

• 26D05: Inequalities for trigonometric functions and polynomials
• 30E05: Moment problems, interpolation problems
• 42A05: Trigonometric polynomials, inequalities, extremal problems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2013
• Tom: 218
• Numer: 1
• Strony: 27-39

Daty

wydano

2013

Twórcy

autor

Omer Friedland

• Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie (Paris 6), 4 Place Jussieu, 75005 Paris, France

autor

Yosef Yomdin

• Department of Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel

Identyfikatory

DOI

10.4064/sm218-1-2