Talk:Generalized function

message: It took me some time to notice 
the
edit of the introduction by C.M.,
but I do not agree at all:
* neither in Schwartz distributions, nor any other theory mentioned (nonstandard, Colombeau), the generalized functions are R- or C-valued. So the first added phrase is at least misleading.
* one can well generalize other structures than numerical functions: this is the case in QFT, the main application field of these theories (where the objects to be generalized are operators on Fock spaces)
* the second phrase "what is generalized is some operator aspect of functions" is not very illuminating (imho). I don't understand what it could mean.
Summarizing, it appears to me that neither of the two phrases is very useful, and I think that the original formulation (see given "diff" link above) is at the same time quite easily understandable, sufficiently precise and still general enough to be correct.
Of course I greatly appreciate the added sections on "early history".
— MFH: Talk 14:34, 23 May 2005 (UTC)
replies: text: First point - I was just trying to say that in generalised function, one does mean generalised numerical function (not for f:X → Y for any sets). Perhaps this could be expressed better, though. Second point, on operators. This is not so much for pure mathematicians, as for computer scientists, physicists and so on. It is meant to be read with the discussion at operator; is an operator not just some kind of function? Well, not exactly. So I defend this as a general thought. More work is probably needed on the introduction. Charles Matthews 15:20, 23 May 2005 (UTC)
thread_title: Introduction and history

message: Once again, I advocate in favour of my earlier formulation,
"making discont. functions differentiable and, which is related, describing point charges", rather than : 
 Generalized functions are especially useful in making
 discontinuous functions more like smooth functions,
 and (going to extremes) describing physical phenomena such as
 point charges.
*Indeed distributions are really in no point like smooth functions, they don't even have a value in each point. The only truth is that they are infinitely differentiable.
*Second, I insist that "making discont. fcts derivable" is related to "describing point charges", if not the same, and the latter is not "going to extremes". Indeed, what is a point change (say, unit charge at the origin)? It is a "density" \rho such that \int_{-\infty}^x \rho(t) dt  is equal to zero for all x<0, and equal to one for all x>0. So the point charge \rho is exactly the derivative of the most simple discont. fct which is Heaviside's fct.
Next paragraph:
 A common feature of some of the approaches
(somehow contradition in itself, imho)
 is that they build on operator aspects of everyday, numerical functions.
I can't see what this explains ("they build on .. aspects": I think this it quite obscure - unless being more precise, I'm against putting this here), and once again, it is not true, since distibutions are in the main field of their application (QFT) operator-valued, and thus not numerical functions.
I'm sorry if I appear too critical (or even unpolite, really sorry for that, I can't help!), and I have not the slightest doubt in your mathematical competence (on the contrary), but I don't appreciate too much changes which are not clearly an improvement of the previous formulation.
I would really appreciate if the latter would be left untouched in its place, and if s.o. wants to add explanations, they would be added in a separate section.
Once again, I really prefer leaving the intro in my original formulation, quite short and "easy to read" at a first glance. I would have nothing against putting your precisions in a following "Motivations" or "Basic ideas" section or so, and even develop them further.
Thanks in advance for your comprehension! — MFH: Talk 13:28, 27 May 2005 (UTC)
thread_title: still in favour of orig.formulation

message: The article distribution (mathematics) seems to be focused on the same topics of this article. —The preceding unsigned comment was added by 80.180.174.104 (talk) 02:11, 10 March 2007 (UTC)
thread_title:  Another WP's article about the same topics 

message: should this be merged with https://en.wikipedia.org/wiki/Distribution_(mathematics)?  — Preceding unsigned comment added by CoincidentalBystander (talk • contribs) 11:21, 13 April 2017 (UTC)
thread_title:  merge with distribution?