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Results 1 - 3 of 3 |
1. CMB 2011 (vol 56 pp. 326)
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Restricting Fourier Transforms of Measures to Curves in $\mathbb R^2$ We establish estimates for restrictions to certain curves in $\mathbb R^2$ of the Fourier transforms
of some fractal measures.
Keywords:Fourier transforms of fractal measures, Fourier restriction Categories:42B10, 28A12 |
2. CMB 2010 (vol 54 pp. 172)
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Measures with Fourier Transforms in $L^2$ of a Half-space
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.
Categories:42B10, 28A75 |
3. CMB 2005 (vol 48 pp. 260)
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A Restriction Theorem for a \\$k$-Surface in $\mathbb R ^n$ We establish a sharp Fourier restriction estimate
for a measure on a $k$-surface in $\mathbb R ^n$, where $n=k(k+3)/2$.
Keywords:Fourier restriction Category:42B10 |