Timeline for Proof without distributions
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 12, 2017 at 21:20 | answer | added | paul garrett | timeline score: 2 | |
| Mar 12, 2017 at 18:36 | comment | added | Yemon Choi | A belated comment: I like this question, and the stated motivation. There are some calculations/questions in abstract harmonic analysis where it is -- for me at least -- more pleasing to use Plancherel and other $L^2$-techniques rather than $C^\infty$ or distributional techniques. Sometimes these suggest generalizations to locally compact groups that aren't Lie, and where Lie approximation seems a bit of a heavy machine | |
| Mar 12, 2017 at 18:18 | answer | added | Phil Isett | timeline score: 7 | |
| Nov 16, 2015 at 1:16 | review | Close votes | |||
| Nov 16, 2015 at 11:54 | |||||
| Nov 15, 2015 at 21:33 | comment | added | Fan Zheng | @user82546 I suspect you can't get something for nothing. Either you use distribution theory (which is abstract but powerful) or you perform tedious calculations (which is elementary but ... tedious). An example of the latter is to mollify $f$ at 0, show the identity in this case, and then show that it converges in the right sense to the right limit. Distribution theory is created precisely to automate/abstract away this tedious process. | |
| Nov 15, 2015 at 19:32 | comment | added | user82546 | @JohannesHahn it is not directly related to a research problem (as so many question on this page are), but it can be used to get the fundamental solution of Laplace's equation very straightforwardly by fourier transform methods without the use of distribution theory or tedious calculations and i considered this as intersting. | |
| Nov 15, 2015 at 19:21 | comment | added | Johannes Hahn | Also note that MO is for research-level questions. In what way did this come up in your research? What goal would such a proof serve? What are you trying to do with it? As stated right now, one might interpret your question as "I have this homework problem but all solutions I found with google use stuff that wasn't covered in my course" which wouldn't be an appropriate question for this site. | |
| Nov 15, 2015 at 19:18 | comment | added | Johannes Hahn | That does not answer my question. There are a lot of questions that can be stated without X, yet one/some/all/the best/the most famous/... proof(s) use X. Especially if X is unconnected to the original question, this is often considered a good thing because it reveals non-trivial connections between different parts of mathematics. Here on the other hand, you want to exclude a theory that is literally made for handling questions about fourier transforms. Why would you want to do that? Do you have a specific goal in mind? | |
| Nov 15, 2015 at 19:11 | comment | added | user82546 | @JohannesHahn as I explained in the question. It is a problem that you can state without distribution theory, but it seems that a solution to the problem requires these methods cause I could not find a proof of this with elementary methods | |
| Nov 15, 2015 at 19:09 | comment | added | Johannes Hahn | And why are you interested in that? | |
| Nov 15, 2015 at 18:54 | history | edited | user82546 | CC BY-SA 3.0 |
added 2 characters in body; edited title
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| Nov 15, 2015 at 17:50 | history | asked | user82546 | CC BY-SA 3.0 |