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- W1660314084 abstract "Inspired by work of Montgomery on Fourier series and Donoho-Strak in signal processing, we investigate two families of rearrangement inequalities for the Fourier transform. More precisely, we show that the $L^2$ behavior of a Fourier transform of a function over a small set is controlled by the $L^2$ behavior of the Fourier transform of its symmetric decreasing rearrangement. In the $L^1$ case, the same is true if we further assume that the function has a support of finite measure. As a byproduct, we also give a simple proof and an extension of a result of Lieb about the smoothness of a rearrangement. Finally, a straightforward application to solutions of the free Shrodinger equation is given." @default.
- W1660314084 created "2016-06-24" @default.
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- W1660314084 date "2011-01-01" @default.
- W1660314084 modified "2023-09-27" @default.
- W1660314084 title "On the Fourier transform of the symmetric decreasing rearrangements" @default.
- W1660314084 hasPublicationYear "2011" @default.
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