Let the Fourier transform be defined by $\hat f(\xi)=\int_{R^n}f(x)e^{-ix\xi}dx$.
Suppose $f\in L^1(R^n)$. How to prove $\hat f$ is uniformly continuous in $R^n$?
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You should check out the related posts – Tim kinsella Dec 13 '14 at 18:42
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@Timkinsella Thanks! I found this post is similar. http://math.stackexchange.com/questions/68642/fourier-transform-is-uniformly-continuous?rq=1 – Sherry Dec 13 '14 at 18:42