An observation on the Turán-Nazarov inequality

Details An observation on the Turán-Nazarov inequality An observation on the Turán-Nazarov inequality

2011-06-30

arxiv.org/abs/1107.0039v2

Mathematics

Functional Analysis

Scientific paper

The main observation of this note is that the Lebesgue measure $\mu$ in the Tur\'an-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 in the original Tur\'an-Nazarov inequality, they necessarily enter the definition of $\omega$.

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