An observation on the Turán–Nazarov inequality
Studia Mathematica, Tome 218 (2013) no. 1, pp. 27-39
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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 $.
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
Affiliations des auteurs :
Omer Friedland 1 ; Yosef Yomdin 2
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author = {Omer Friedland and Yosef Yomdin},
title = {An observation on the {Tur\'an{\textendash}Nazarov} inequality},
journal = {Studia Mathematica},
pages = {27--39},
publisher = {mathdoc},
volume = {218},
number = {1},
year = {2013},
doi = {10.4064/sm218-1-2},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm218-1-2/}
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Omer Friedland; Yosef Yomdin. An observation on the Turán–Nazarov inequality. Studia Mathematica, Tome 218 (2013) no. 1, pp. 27-39. doi: 10.4064/sm218-1-2
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