Delta function defined for complez values

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

[tex] \delta (x-a-bi) [/tex] or [tex] \delta (-ix) [/tex]

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

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

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

[tex] \delta (x-a-bi) [/tex] or [tex] \delta (-ix) [/tex]

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

[tex] \delta (ix) = \delta(x) [/tex] 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.
 

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