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Admiraldesvl / Admiraldesvl.github.io

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The Fourier Transform of exp(-cx^2) and Its Convolution - Desvl's blog #5

Open utterances-bot opened 1 year ago

utterances-bot commented 1 year ago

The Fourier Transform of exp(-cx^2) and Its Convolution - Desvl's blog

We develop two almost straightforward way to compute the Fourier transform of $\exp(-cx^2)$, in the sense that any contour integration and the calculus of residues are not required at all. The first c

https://desvl.xyz/2022/05/06/exp-fourier/

Ryan-Mabrey commented 1 year ago

When you write "This differential equation corresponds to an integral equation" are you allowed to integrate with respect to two vairiables? Could you please explain how it corresponds to the integral equation more in depth? Thanks!

Admiraldesvl commented 1 year ago

When you write "This differential equation corresponds to an integral equation" are you allowed to integrate with respect to two vairiables? Could you please explain how it corresponds to the integral equation more in depth? Thanks!

@Ryan-Mabrey The equation you asked is understood as a seperable equation. See section 1.3.1 of this note for a rigourous explanation. Turn to theorem 1.3.2 of the note, you see $h(\varphi)=2c\frac{1}{\varphi}$ and $g(t)=-t$.

Admiraldesvl commented 1 year ago

If math formula is not loading, view the reply on github