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Results tagged with fourier-analysis
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user 16702
The representation of functions (or objects which are in some generalize the notion of function) as constant linear combinations of sines and cosines at integer multiples of a given frequency, as Fourier transforms or as Fourier integrals.
1
vote
Fourier Transform, for entire function
The Fourier Transform $\mathcal{F}$ is at first defined on the Schwartz space $\mathcal{S}$ and is a linear isomorphism there. As always, there is a dual operator $\mathcal{F}^\prime$ that is an isomo …
- 9,853
15
votes
4
answers
2k
views
Positivity of certain Fourier transform
Is the Fourier transform of the function
$$ f(\xi) = e^{-t|\xi|^{2m}}$$
positive for $t>0$ and $m \in \mathbb{N}_0$?
- 9,853