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 $\displaystyle f(x) = x^2 - a^2$ then $\displaystyle f'(x) = 2x$.
Now the zeros are: $\displaystyle -a,a$, assuming $\displaystyle a\not = 0$.
Thus, $\displaystyle \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] $