Lacunary Fourier series and a qualitative uncertainty principle for compact Lie groups
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We define lacunary Fourier series on a compact connected semisimple Lie group G. If f ∈ 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.
Keywords.Lacunary Fourier series; uncertainty principles; Weyl’s character formula.
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