On the Fourier transform of the symmetric decreasing rearrangements

Details On the Fourier transform of the symmetric decreasing rearrangements On the Fourier transform of the symmetric decreasing rearrangements

2008-09-03

arxiv.org/abs/0809.0604v1

Annales de l'Institut Fourier (2010) a paraitre

Mathematics

Classical Analysis and ODEs

Scientific paper

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 Shr\"odinger equation is given.

Affiliated with

Also associated with

No associations

Rating

On the Fourier transform of the symmetric decreasing rearrangements does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the Fourier transform of the symmetric decreasing rearrangements, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Fourier transform of the symmetric decreasing rearrangements will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-104573