Lacunary Fourier series and a qualitative uncertainty principle for compact Lie groups

Details Lacunary Fourier series and a qualitative uncertainty principle for compact Lie groups Lacunary Fourier series and a qualitative uncertainty principle for compact Lie groups

2010-07-07

arxiv.org/abs/1007.1027v1

Mathematics

Functional Analysis

Scientific paper

We define lacunary Fourier series on a compact connected semisimple Lie group
$G$. If $f \in L^1(G)$ has lacunary Fourier series, and vanishes on a non empty
open set, then we prove that $f$ vanishes identically. This may be viewed as a
qualitative uncertainty principle.

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