An observation on the Turán-Nazarov inequality

Omer Friedland, and Yosef Yomdin. "An observation on the Turán-Nazarov inequality." Studia Mathematica 218.1 (2013): 27-39. <http://eudml.org/doc/286087>.

@article{OmerFriedland2013,
abstract = {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.},
author = {Omer Friedland, Yosef Yomdin},
journal = {Studia Mathematica},
keywords = {metric entropy; Turán-Nazarov inequality},
language = {eng},
number = {1},
pages = {27-39},
title = {An observation on the Turán-Nazarov inequality},
url = {http://eudml.org/doc/286087},
volume = {218},
year = {2013},
}

TY - JOUR
AU - Omer Friedland
AU - Yosef Yomdin
TI - An observation on the Turán-Nazarov inequality
JO - Studia Mathematica
PY - 2013
VL - 218
IS - 1
SP - 27
EP - 39
AB - 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.
LA - eng
KW - metric entropy; Turán-Nazarov inequality
UR - http://eudml.org/doc/286087
ER -