# Complex integral representation of Dirac delta function?

1. Dec 29, 2009

### pellman

We all know that $$\frac{1}{2\pi}\int{e^{ik(x-x')}dk=\delta(x-x')$$.

i am working a problem which appears to depend on the statement

$$\int e^{z^*(z-w)}dz^*\propto\delta(z-w)$$

Does anyone know if this is valid?

$$\delta(z-w)$$ is defined in the usual way so that

$$\int{\delta(z-w)f(z)dz}=f(w)$$

This is a physics problem, though, so the domain of integration is not specified and not clear to me.

2. Jan 2, 2010

3. Jan 3, 2010

### Marin

Hi, pellman

I just saw your thread and remembered reading a similar article on the net. Here it is, I guess it may be helpful:

http://homepages.physik.uni-muenchen.de/~Winitzki/no_distrib_limit.pdf [Broken]

Last edited by a moderator: May 4, 2017
4. Jan 4, 2010

### pellman

That paper is a very good jumping off point. Thank you!