Oscillation of Fourier Integrals with a spectral gap
Classical Analysis and ODEs
2007-05-23 v1 Complex Variables
Abstract
Suppose that Fourier transform of a function f is zero on the interval [-a,a]. We prove that the lower density of sign changes of f is at least a/pi, provided that f is a locally integrable temperate distribution in the sense of Beurling, with non-quasianalytic weight. We construct an example showing that the last condition cannot be omitted.
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Cite
@article{arxiv.math/0301060,
title = {Oscillation of Fourier Integrals with a spectral gap},
author = {A. Eremenko and D. Novikov},
journal= {arXiv preprint arXiv:math/0301060},
year = {2007}
}
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