Re: Impossible sampling theory!

From: Tim Wescott (tim_at_wescottnospamdesign.com)
Date: 12/10/04 

Date: Fri, 10 Dec 2004 08:30:58 -0800

David C. Ullrich wrote:
>>
>>Can you recommend a good website or book?
>
>
> If you want the whole story you need to learn some
> "real analysis" first (measure theory, topological
> vector spaces, etc). There are many places you can
> find the theory of distributions worked out in
> detail - the two that are standard texts where I
> come from would be Folland "Real Analysis" (or
> maybe it's "Real Analysis and Applications" or
> something) and Rudin "Functional Analysis".
>
> Website? Hmm, google...
>
> It seems that wikipedia
>
> http://en.wikipedia.org/wiki/Distribution
>
> discusses the topic, although I doubt that
> there's a complete exposition of the theory
> there, in an "encyclopedia" they must have
> just statements of the main results.
>
> The description of
>
> http://www.math.ku.dk/~grubb/distcon.pdf
>
> on google sounds like it might be what
> you want, but that actual pdf is just a
> table of contents. I didn't see how to find
> the actual notes on the site, but maybe you
> can if you hunt around.
>
> Otoh I wouldn't be surprised if there is no
> web site that actually contains the whole story.
>
> ************************
>
> David C. Ullrich

I have "Intermediate Real Analysis" by Emanuel Fischer, but if it
discusses those topics it does so by entirely different names -- I
rather suspect that it leaves off where your other texts start.

So far any time I've felt a need for rigor around the delta function
(distribution, whatever) I've just constructed some real function with
area one that's either parameterized by height (or width), found my
result, then taken the limit as the parameter goes to infinity (or
zero). It's probably not entirely kosher, but it's served my purposes. 

-- 
Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

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