Sets of uniqueness
Singular distributions, dimension of support, and symmetry of Fourier transform
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:(i) 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 its support;(ii) A construction of compacts of “critical” size, which support distributions (even pseudo-functions) with anti-analytic part belonging to .We also give examples of non-symmetry...
Some spherical uniqueness theorems for multiple trigonometric series.
Sur les isomorphismes d'algèbres de restriction