Dirac-Delta function

From: Adam (addam_at_rogers.com)
Date: 10/03/04 

Date: Sat, 2 Oct 2004 21:41:52 -0400

Hi,

I would like to know what mathematicians think of the Dirac-Delta function.
Also, what the pure mathematics way of writing and defining it would be.

This is how the delta function has been "defined."
Let h denote the delta function.
Integral(-infinity, +infinity)h(x)f(x)dx = f(0).
Integral(-infinity, +infinity)h(x)dx = 1.

I was used to reading things like: "Let f: R -> R denote a function defined
by f(x) = x^2 for all x in R."

The dirac-delta function doesn't really make any sense. I understand that
can be thought of as the limit of ever increasing functions centered at the
origin, but how do pure mathematicians define and describe it?

Please provide a description like "h: R -> R" etc, if possible. The function
seems very strange.

Thanks, Adam.

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