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Community Bot
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The following problem arose in a questiona question I recently asked : given a (possibly non abelian) compact group $G$ and a neighbourhood $U$ of the identity in $G$, can we always find a function $f : G \mapsto \mathbb{R}$, which vanishes outside $U$, whose Fourier transform is nonnegative, and which satisfies $\hat f(1) \neq 0$ ?

The following problem arose in a question I recently asked : given a (possibly non abelian) compact group $G$ and a neighbourhood $U$ of the identity in $G$, can we always find a function $f : G \mapsto \mathbb{R}$, which vanishes outside $U$, whose Fourier transform is nonnegative, and which satisfies $\hat f(1) \neq 0$ ?

The following problem arose in a question I recently asked : given a (possibly non abelian) compact group $G$ and a neighbourhood $U$ of the identity in $G$, can we always find a function $f : G \mapsto \mathbb{R}$, which vanishes outside $U$, whose Fourier transform is nonnegative, and which satisfies $\hat f(1) \neq 0$ ?

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user25235
user25235
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Test functions with small support and nonnegative Fourier transform

The following problem arose in a question I recently asked : given a (possibly non abelian) compact group $G$ and a neighbourhood $U$ of the identity in $G$, can we always find a function $f : G \mapsto \mathbb{R}$, which vanishes outside $U$, whose Fourier transform is nonnegative, and which satisfies $\hat f(1) \neq 0$ ?