Singular distributions, dimension of support, and symmetry of Fourier transform
Classical Analysis and ODEs
2015-03-14 v2
Abstract
We study the "Fourier symmetry" of measures and distributions on the circle, in relation with the size of their supports. The main results of this paper are: (1) A one-side extension of Frostman's theorem, which connects the rate of decay of Fourier transform of a distribution with the Hausdorff dimension of the support; (2) A construction of compacts of "critical" size, which support distributions (even pseudo-functions) with anti-analytic part belonging to l^2. We also give examples of non-symmetry which may occur for measures with "small" support. A number of open questions are stated.
Keywords
Cite
@article{arxiv.1004.3631,
title = {Singular distributions, dimension of support, and symmetry of Fourier transform},
author = {Gady Kozma and Alexander Olevskii},
journal= {arXiv preprint arXiv:1004.3631},
year = {2015}
}
Comments
19 pages, to appear in Ann. Inst. Fourier