Talk:Fourier inversion theorem

message: There is a bunch of broken math code on this page, but I don't know how to fix it.  Someone needs to do this! --Shoofle
:Looks OK to me now.  Try again.  Or maybe try on a different browser?  Maybe just a temporary glitch? Michael Hardy 18:43, 28 August 2006 (UTC)
thread_title:  (talk before TOC) 

message: this is necessary e.g. to read Tate's thesis. i do not have the expertise to do it.  —Preceding unsigned comment added by 76.182.61.207 (talk) 18:09, 14 January 2009 (UTC)
thread_title: article needs explanation of the general case for a locally compact group

message: I don't know if a proof would be appropriate here, but can anyone provide a source that actually includes a proof? Its probably online somewhere, but it has eluded me so far. 146.6.200.213 (talk) 22:27, 11 May 2009 (UTC)
replies: text:  There is a proof in the book "Introduction to Partial Differential Equations" by Gerald Folland, I added a proof here roughly along those lines. He places the 2\pi in a different place, which I followed, I like it better his way. Let me know if anything is unclear or should be changed. Compsonheir (talk) 12:47, 25 June 2009 (UTC)
thread_title:  proof 

message: Which means that the only people who can read it, are those who don’t need it anymore.
Well done. Really. Impressive job! Way to go!
The article just throws formulas in your face, and doesn’t even care to explain the history or examples/problem that it started with. It just vomits symbols and relations without meaning in your face.
Maybe you mathematician-types understand this better: For any real human, this article is not is the set of understandable articles, for any time or space location in all of space-time!
Read up on this article that explains how you can make a concept understandable for actual real humans!
Conclusion: You massively, epically and horribly fail! At remaining an actual real human, and at making useful articles.
— 94.220.250.151 (talk) 23:34, 16 October 2009 (UTC)
thread_title:  The article is ''completely '''useless''''' for any non-mathematician. 

message: I believe the integral in the last part of the proof of the theorem should read:
:\lim_{\varepsilon\to 0}\int e^{2\pi i x\cdot\xi}\widehat{f}(\xi)e^{-\pi\varepsilon^2|\xi|^2}d\xi
Nice article, and I think there is a good point for its existence. Why there is no reference to it by the other Fourier-related articles?  —Preceding unsigned comment added by 79.129.223.145 (talk) 10:28, 29 July 2010 (UTC)
thread_title:  error? 

message: for the dominated convergence theorem, should'nt it be f\in L^1(\mathbb{R}^n) instead of \mathcal{F}f\in L^1(\mathbb{R}^n)?
For \varepsilon\leq 1 we have
: \left| e^{-\pi\varepsilon^2|\xi|^2 + 2\pi i x\cdot\xi}(\mathcal{F}f)(\xi)\right| = e^{-\pi\varepsilon^2|\xi|^2}|(\mathcal{F}f)(\xi)|\leq e^{-\pi|\xi|^2}|(\mathcal{F}f)(\xi)|=:g(\xi) ,
so if g\in L^1(\mathbb{R}^n), this would work as our dominating function.
This is true, since
: \int_{\mathbb{R}^n} g(\xi)\,d\xi \leq \|\mathcal{F}f\|_{L^\infty(\mathbb{R}^n)} \int_{\mathbb{R}^n} e^{-\pi|\xi|^2}\,d\xi \leq \|f\|_{L^1(\mathbb{R}^n)} <\infty.
Headfime (talk) 15:34, 16 December 2017 (UTC)
thread_title:  Error in the proof