Answer by Christian Remling for Is there a compactly supported differentiable...
Yes, such differentiable compactly supported functions $G$ with $\widehat{G}\notin L^1$ exist. This follows from the fact the Fourier transform is not bounded as a map from $\{f\in C[0,1]:...
View ArticleAnswer by actions for Is there a compactly supported differentiable function...
This is a comment, not an answer, but I am not entitled. The (inverse) fourier transforms of smooth functions with compact support are described precisely in the Paley-Wiener-Schwartz theorem, the...
View ArticleIs there a compactly supported differentiable function whose Fourier...
In my MSE answer here, I discussed the example of compactly supported continuous function$$g(x)=\begin{cases}\dfrac{\frac12 -x}{\log(x)},&0<x\leq1/2\\0,&\text{otherwise}\end{cases}$$which is...
View Article
More Pages to Explore .....
