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

2010/07/07 by E K Narayanan, Narayanan, E K, Alladi Sitaram +2
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Mathematical Analysis and Transform Methods #math.FA

paper · pdf · doi:10.48550/arxiv.1007.1027

arxiv created 2010/07/07 · arxiv updated 2010/07/08

Abstract

We define lacunary Fourier series on a compact connected semisimple Lie group G. If f ∈ L¹(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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