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Results tagged with fourier-transform
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user 169474
4
votes
Accepted
Asking for reference about a relation related to Fourier transform
If $f_1,\ldots,f_n$ belong to the Schwarz space, Fourier inversion formula and Fourier-convolution properties yield
\begin{eqnarray*}
\int_{\xi_1+\cdots+\xi_n=0} \hat{f_1}(\xi_1) \cdots \hat{f_n}(\xi_ …
- 3,808
3
votes
Accepted
Decay of the Fourier transform of a non-differentiable function
I answer question $(1)$, assuming only that $\varphi$ is integrable.
If $(1)$ holds, then $\hat{\varphi}$ is also integrable, so Fourier inversion formula applies. For almost every $x \in \mathbb{R}$, …
- 3,808