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Measures with Fourier Transforms in $L^2$ of a Half-space |
Canad. Math. Bull. 54(2011), 172-179
Published:2010-07-26
Printed: Mar 2011
Printed: Mar 2011
- Bassam Shayya,
Abstract
We prove that if the Fourier transform of a compactly supported
measure is in $L^2$ of a half-space, then the measure is
absolutely continuous to Lebesgue measure. We then show how this
result can be used to translate information about the
dimensionality of a measure and the decay of its Fourier
transform into geometric information about its support.
| MSC Classifications: |
42B10 - Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type 28A75 - Length, area, volume, other geometric measure theory [See also 26B15, 49Q15] |