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29 March 2024
 
  » arxiv » math.CA/0301060

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Oscillation of Fourier Integrals with a spectral gap
A. Eremenko ; D. Novikov ;
Date 7 Dec 2002
Subject Classical Analysis and ODEs; Complex Variables MSC-class: 42A38 46F12 46F20 | math.CA math.CV
AbstractSuppose 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.
Source arXiv, math.CA/0301060
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