Seeking Text On Distributions

1. Nov 29, 2004

cjellison

Hi, I am not seeking a "complete" treatment of distribution functions (like Gelfand or Schwartz). However, I would like some discussion in regards to multiplying delta functions together---especially in QM.

From the little I have discovered, distributions do not form an algebra, and thus, one cannot "legally" multiply delta functions together. However, we do this all the time:

$$\delta(\mathbf{r}-\mathbf{r}_0) = \delta(x-x_0)\delta(y-y_0)\delta(z-z_0)$$

Also, I was wondering about a text that discussed in detail the problem with "complete" sets of eigenfunctions in an infinite-dimensional space ($L_2$) and normalizing to a delta function rather than to 1. I guess I am looking for better explanations than the typical "it just works" explanation. Do I need von Neumann's book?

Thanks.