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Search: MSC category 42B10 ( Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type )

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1. CMB 2011 (vol 56 pp. 326)

Erdoğan, M. Burak; Oberlin, Daniel M.
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)

Shayya, Bassam
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)

Oberlin, Daniel M.
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

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