A version of the Uncertainty Principle for functions with lacunary Fourier transforms

[摘要] We prove estimates of the L-2 norms on relatively dense subsets of the real line of functions with Fourier transforms supported on lacunary sets of intervals. This result is a real line analogue of Zygmund's theorem on lacunary trigonometric series. The results also hold in higher dimensions. (C) 2003 Elsevier Inc. All rights reserved.

[发布日期] 2003-12-15

[关键词] Uncertainty principle;Logvinenko-Sereda theorem;lacunary series;relatively dense sets