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

E K Narayanan; A Sitaram

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arXiv · 1007.1027

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

E K Narayanan·A Sitaram

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Abstract

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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BibTeX RIS

E K Narayanan, A Sitaram. 2010-07-07. Lacunary Fourier series and a qualitative uncertainty principle for compact Lie groups. https://arxiv.org/abs/1007.1027

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