Delta function defined for complez values

[mhill]

is there a form to define the dirac delta function for complex values ? i mean

$$\delta (x-a-bi)$$ or $$\delta (-ix)$$

using 'test functgions' i get that they converge nowhere (always infinite) which makes no sense at all, using scalling properties we could define

$$\delta (ix) = \delta(x)$$ since modulus of 'i' is just one but i am not completely sure.

 

[mathman]

is there a form to define the dirac delta function for complex values ? i mean

$$\delta (x-a-bi)$$ or $$\delta (-ix)$$

using 'test functgions' i get that they converge nowhere (always infinite) which makes no sense at all, using scalling properties we could define

$$\delta (ix) = \delta(x)$$ since modulus of 'i' is just one but i am not completely sure.

In using the delta function, the domain is the real line. There is no problem with using it with a complex constant or even multiplying x by i. Just be careful about what problem you are trying to solve. Remeber the delta function makes sense only under integral signs.