- #1

CptXray

- 23

- 3

## Homework Statement

Let ##T## be a distribution in ##\mathcal{D}(\mathbb{R}^2)## such that:

$$T(\phi) = \int_{0}^{1}dr \int_{0}^{\pi} \phi(r, \Phi)d\Phi$$

$$\phi \in \mathcal{D}(\mathbb{R}^2)$$

calculate ##r \frac{\partial{}}{\partial{r}} \frac{\partial{}}{\partial{\Phi}}T##.

## Homework Equations

## The Attempt at a Solution

I think it has something to do with the fact that derivative of a distribution is defined with some test function ##\theta##, such that: ##T \theta' = -T' \theta##. And in more general case: ##T^{(\alpha)}\theta = (-1)^{\alpha} T \theta^{(\alpha)}##. Here for ##A(x)##: ##A^{(\alpha)} = \frac{\partial{A}}{\partial{x}}##. But here i have two derivatives of different parameters and also ##r##. I've found literature about distributions (quite few to be honest) but can't find any examples that could help me do the calculations and get the feeling about this. I'd be grateful for help and tips.