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发帖数: 33 | 1 (Sorry I have no Chinese now)
Here delta(t) is defined as usual in math/physics:
Integral(delta(t),t=-infinity,+infinity)=1,
Integral(delta(t)*f(t),t)=f(0), where f(t) is any function.
Now what is:
Integral(delta(t)^2,t=-infinity,+infinity)=?
should it equals to delta(0) and thus not well defined?
Thanks. | l**********n
发帖数: 72 | 2 One simple example for the Delta function:
e approaches zero: 1/(2*pi*e)^0.5*exp(-(x^2)/2e^2), it's the
Gaussian distribution in 1D and as e approaches zero, it
becomes delta function. So as you can see from your example,
after you square the funtion, the denominator becomes 1/e
and it simply diverge at zero after integration.
Delta square function can be regularized by some technique
and if it's only the intermediate step in your calculations,
you can take it as the funtion proposed here. You c |
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