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Results tagged with fourier-transform
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user 37103
0
votes
Estimate a Fourier Transform
$$2if(x_1,x_2)=(e^{i\langle N_1,x\rangle}-e^{-i\langle N_1,x\rangle})h(g^{-1}(x))$$
so
$$2i\hat f(\omega)=\widehat{h\circ g^{-1}}(\omega-N_1)-\widehat{h\circ g^{-1}}(\omega+N_1).$$
Since $h$ is smooth …
- 5,169
2
votes
Accepted
Solution to inhomogenous PDE
This kernel is called the Bessel potential. It is smooth away from $0$, and in your case, this kernel is locally integrable.
- 5,169
4
votes
Accepted
Fourier transform inversion theorem for a function not in L1 or L2
You can define the distributionial Fourier transform of a tempered distribution using all the abstract machinery established by Schwartz, and the thing you want to check is that it agrees with the int …
- 5,169