Does the Dirac measure still exist on a complex domain?

1. Jan 2, 2010

friend

does the Dirac measure still exist with complex variance?

The Dirac delta function can be rigorously defined as a measure. See

http://en.wikipedia.org/wiki/Dirac_delta_function#As_a_measure

For the gaussian form of the Dirac delta function we have,

$$${\rm{\delta (x - x}}_0 ) = \mathop {\lim }\limits_{\Delta \to 0} \frac{1}{{(2\pi \Delta )^{1/2} }}e^{ - (x - x_0 )^2 /(2\Delta )}$$$

with variance $$\Delta$$.

My question is whether the gaussian from of the Dirac delta is still a measure if the variance is complex. Any insight about this would be appreciated.

Last edited: Jan 2, 2010