We define lacunary Fourier series on a compact connected semisimple Lie group 𝐺. If $f\in L^1(G)$ has lacunary Fourier series and 𝑓 vanishes on a non empty open subset of 𝐺, then we prove that 𝑓 vanishes identically. This result can be viewed as a qualitative uncertainty principle.
Volume 131, 2021
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