For some reason I cant post everything at once... gives me a "Database error" so I will post in parts...(adsbygoogle = window.adsbygoogle || []).push({});

A vector function can be decomposed to form a curl free and divergence

free parts:

[tex]\vec{f}(\vec{r})=\vec{f_{\parallel}}(\vec{r'})+\vec{f_{\perp}}(\vec{r'})[/tex]

where

[tex]\vec{f_{\parallel}}(\vec{r'}) = - \vec{\nabla} \left( \frac{1}{4 \pi} \int d^3 r' \frac{\vec{\nabla'} \cdot \vec{f}(\vec{r'})}{|\vec{r}-\vec{r'}|} \right)[/tex]

and

[tex]\vec{f_{\perp}}(\vec{r'}) = \vec{\nabla} \times \left( \frac{1}{4 \pi} \int d^3 r' \frac{\vec{\nabla'} \times \vec{f}(\vev{r'})}{|\vec{r}-\vec{r'}|}[/tex]

I am trying to take the Fourier transform of [itex]\vec{f_{\parallel}}(\vec{r'})[/itex] and [itex]\vec{f_{\perp}}(\vec{r})[/itex]

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# Fourier transform

Can you offer guidance or do you also need help?

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