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arXiv · 1004.3631

Singular distributions, dimension of support, and symmetry of Fourier transform

Gady Kozma·Alexander Olevskii
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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.

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Gady Kozma, Alexander Olevskii. 2011-01-25. Singular distributions, dimension of support, and symmetry of Fourier transform. https://arxiv.org/abs/1004.3631

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