Oscillation of Fourier Integrals with a spectral gap

Details Oscillation of Fourier Integrals with a spectral gap Oscillation of Fourier Integrals with a spectral gap

2003-01-07

arxiv.org/abs/math/0301060v1

Mathematics

Classical Analysis and ODEs

1 Figure

Scientific paper

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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