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Oct
17
comment Dirac Delta definition in non-standard analysis?
Delta is even function so its derivative should be odd. That is zero at x=0.
Oct
17
comment Dirac Delta definition in non-standard analysis?
@Hurkyl if derivative of delta is negative at x<0 and positive at x>0, this means that delta is non-positive around and in zero, which would not give positive integral. It is evident you made a mistake.
Oct
17
comment Dirac Delta definition in non-standard analysis?
@Hurkyl it seems you confused the right and left parts of the function in this definition of derivative. Its derivative should be positive at negative part and negative at positive area, otherwise its integral would be negative. Also note that this definition has a major disadvantage: delta is even function so its derivative shoud be odd. And also it should be 0 in x=0 because delta has maximum there.
Oct
17
comment Dirac Delta definition in non-standard analysis?
it is differentiable in a sense. At least, the notion of derivative of dirac delta (and further derivatives) is widely used. See my answer for the for that I found is employed in non-standard analysis. Its derivative thus would be $-\frac{2 w^3 z e^{-(w z)^2}}{\sqrt{\pi }}$
Oct
17
revised Dirac Delta definition in non-standard analysis?
edited body
Oct
17
comment Dirac Delta definition in non-standard analysis?
this has only a few properties of Dirac Delta and does not have others (i.e. differentiability).
Oct
17
revised Dirac Delta definition in non-standard analysis?
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Oct
17
comment Dirac Delta definition in non-standard analysis?
How would u differentiate such delta function?
Oct
17
comment Dirac Delta definition in non-standard analysis?
@Semiclassical this is what is non-standard analysis. And also $\delta(0)=\frac{\omega}{\sqrt{\pi}}$
Oct
17
revised Dirac Delta definition in non-standard analysis?
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Oct
17
answered Dirac Delta definition in non-standard analysis?
Oct
16
revised Dirac Delta definition in non-standard analysis?
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Oct
16
asked Dirac Delta definition in non-standard analysis?
Oct
15
comment Obtaining generating function via Fourier transform
@Semiclassical yes but I wonder whether it is possible using Fourier transform.
Oct
15
asked Obtaining generating function via Fourier transform
Oct
14
awarded  Yearling
Oct
14
comment Fourier transform of exponent?
@Inquisitive this exactly follows from the first formula in the question so what?
Oct
14
comment Fourier transform of exponent?
@Inquisitive because integral of that function along the real line is 0.
Oct
14
asked Dirac Delta of complex argument
Oct
14
asked Fourier transform of exponent?