Can someone explain or provide a reference to a treatment of the well known Dirac delta function which places it on a better foundation (not too rigorous!) than a switching of orders of integration or of limit taking?
An expression of the delta function that particularly interests me is the Fourier transform of the function f(x) = 1.
I'll just plod along. Thanks!
Well, like I said, I'd say the sifting property is the best way to think about the Dirac Delta "function". Under an integration, the Dirac Delta function "picks out" the value of the function at the point where the argument of the Dirac Delta function is zero.