The Uncertainty Principle for relatively dense sets and lacunary spectra
arXiv:math/0212129
Abstract
We obtain a new version of the Uncertainty Principle for functions with Fourier transforms supported on a lacunary set of intervals. This is a generalization of Zygmund's theorem on lacunary trigonometric series to the real line in the spirit of the Logvinenko-Sereda theorem for relatively dense sets.