Re: help with dirac delta function ?

pagcal a écrit :
Can someone offer help understanding properties of the dirac delta function?

given

integ(delta(alpha*x)) = integ(delta(u)du/|alpha|) = 1/|alpha|

In the second term, how did magnitude alpha appear and in the
denominator?

integ is integral +infinity to -infin


It's the classical change of variable (for alpha <> 0) t = alpha*x
in the initial integral : int_{-oo}^oo delta(alpha*x) dx
to get
if alpha>0
int_{-oo}^oo delta(t) dt/alpha
if alpha<0
int_{+oo}^{-oo} delta(t) dt/alpha

that is for alpha <> 0
int_{-oo}^oo delta(t) dt/|alpha|
= 1/|alpha|

hoping it helped,
Raymond
.

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