@article {Eremenko5872,
author = {Eremenko, A. and Novikov, D.},
title = {Oscillation of functions with a spectral gap},
volume = {101},
number = {16},
pages = {5872--5873},
year = {2004},
doi = {10.1073/pnas.0302874101},
publisher = {National Academy of Sciences},
abstract = {We prove an old conjecture on oscillation of functions that have a spectral gap at the origin. Suppose that the Fourier transform of a real measure f on the real line satisfies f̂(x) = 0 for x ∈ ({\textendash}a, a). Then, when r {\textrightarrow} $\infty$, the asymptotic lower density of the sequence of sign changes of f on the intervals [0, r) is at least a/π. This still holds for some wider classes of measures characterized by their rate of growth at infinity, but if the growth is faster than a certain threshold, the above statement is no longer true.},
issn = {0027-8424},
URL = {https://www.pnas.org/content/101/16/5872},
eprint = {https://www.pnas.org/content/101/16/5872.full.pdf},
journal = {Proceedings of the National Academy of Sciences}
}