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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.
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 -