# Lacunary Fourier series and a qualitative uncertainty principle for compact Lie groups - Mathematics > Functional Analysis

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

Author: E K Narayanan, A Sitaram

Source: https://arxiv.org/