1. ## delta function

Hi,

so i am having trouble expressing the function delta(X^2-a^2) as a sum of delta functions.....?

thanks.

so far i have something which includes my test function multiplied by the delta function?? is that right at all?

2. Originally Posted by pepe
Hi,

so i am having trouble expressing the function delta(X^2-a^2) as a sum of delta functions.....?

thanks.

so far i have something which includes my test function multiplied by the delta function?? is that right at all?
Let $f(x) = x^2 - a^2$ then $f'(x) = 2x$.
Now the zeros are: $-a,a$, assuming $a\not = 0$.

Thus, $\delta (f(x)) = \frac{\delta(x+a)}{|f'(-a)|} + \frac{\delta(x-a)}{|f'(a)| } = \frac{1}{2|a|} \left[ \delta(x+a) + \delta (x-a) \right]$