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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
Hrm, I see the same thing. The error reads: "Failed to parse (Can't write to or create math output directory): ..." Funny thing is, when I look through the history, even the current version doesn't give the same error. Edit this page/preview also 'fails' to show an error! Not sure how or why this is borfing like this. Btw, I'm getting the same error in Safari and Opera, but this doesn't seem like a problem is happening client-side. — gogobera ( talk) 23:13, 17 May 2007 (UTC)
When discussing the Fourier inversion for L1 functions we have the statement
And I am concerned about the content here. I don't believe that the above limit exists for general L1 function. (My reasons being that the corresponding statement is not true for Fourier series, as shown by Kolmogorov, and the Hilbert transform is not bounded on L1). Is there a reference for this? Thenub314 ( talk) 14:59, 8 October 2008 (UTC)
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)
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)
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)
What? I am 12 and I can understand it. This is one of the clearest articles on all of Wikipedia. — Preceding unsigned comment added by 220.255.2.55 ( talk) 03:37, 26 November 2011 (UTC)
Despite the crass way that someone said this above, this article could actually do with significant improvement (but despite what that guy said, it's fantastic start). Here are problems that I see, and suggestions to fix them:
Quietbritishjim ( talk) 17:43, 2 March 2010 (UTC)
I believe the integral in the last part of the proof of the theorem should read:
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)
Right about the error, I fixed it. Compsonheir ( talk) 03:46, 1 March 2011 (UTC)
I have mostly rewritten this article. I haven't tried to make the perfect article, only one that's better than the current one. The new version is currently over at User:Quietbritishjim/Fourier_inversion_theorem, but before I move it over here I'm giving fair warning so anyone interested can voice their comments / objections.
Here is a summary of the changes (and things that haven't changed):
Extended content
|
---|
Fourier transforms of square-integrable functions Plancherel theorem allows the Fourier transform to be extended to a unitary operator on the Hilbert space of all square-integrable functions, i.e., all functions satisfying Therefore it is invertible on L2. In case f is a square-integrable periodic function on the interval , it has a Fourier series whose coefficients are The Fourier inversion theorem might then say that What kind of convergence is right? "Convergence in mean square" can be proved fairly easily: What about convergence almost everywhere? That would say that if f is square-integrable, then for "almost every" value of x between 0 and 2π we have This was not proved until 1966 in (Carleson, 1966). For strictly finitary discrete Fourier transforms, these delicate questions of convergence are avoided.
|
So I think my proposed new article is a bit flawed but an improvement on the current situation. Quietbritishjim ( talk) 01:10, 31 December 2012 (UTC)
for the dominated convergence theorem, should'nt it be instead of ?
For we have
so if , this would work as our dominating function. This is true, since
![]() | This article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
|
![]() | This article links to one or more target anchors that no longer exist.
Please help fix the broken anchors. You can remove this template after fixing the problems. |
Reporting errors |
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
Hrm, I see the same thing. The error reads: "Failed to parse (Can't write to or create math output directory): ..." Funny thing is, when I look through the history, even the current version doesn't give the same error. Edit this page/preview also 'fails' to show an error! Not sure how or why this is borfing like this. Btw, I'm getting the same error in Safari and Opera, but this doesn't seem like a problem is happening client-side. — gogobera ( talk) 23:13, 17 May 2007 (UTC)
When discussing the Fourier inversion for L1 functions we have the statement
And I am concerned about the content here. I don't believe that the above limit exists for general L1 function. (My reasons being that the corresponding statement is not true for Fourier series, as shown by Kolmogorov, and the Hilbert transform is not bounded on L1). Is there a reference for this? Thenub314 ( talk) 14:59, 8 October 2008 (UTC)
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)
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)
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)
What? I am 12 and I can understand it. This is one of the clearest articles on all of Wikipedia. — Preceding unsigned comment added by 220.255.2.55 ( talk) 03:37, 26 November 2011 (UTC)
Despite the crass way that someone said this above, this article could actually do with significant improvement (but despite what that guy said, it's fantastic start). Here are problems that I see, and suggestions to fix them:
Quietbritishjim ( talk) 17:43, 2 March 2010 (UTC)
I believe the integral in the last part of the proof of the theorem should read:
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)
Right about the error, I fixed it. Compsonheir ( talk) 03:46, 1 March 2011 (UTC)
I have mostly rewritten this article. I haven't tried to make the perfect article, only one that's better than the current one. The new version is currently over at User:Quietbritishjim/Fourier_inversion_theorem, but before I move it over here I'm giving fair warning so anyone interested can voice their comments / objections.
Here is a summary of the changes (and things that haven't changed):
Extended content
|
---|
Fourier transforms of square-integrable functions Plancherel theorem allows the Fourier transform to be extended to a unitary operator on the Hilbert space of all square-integrable functions, i.e., all functions satisfying Therefore it is invertible on L2. In case f is a square-integrable periodic function on the interval , it has a Fourier series whose coefficients are The Fourier inversion theorem might then say that What kind of convergence is right? "Convergence in mean square" can be proved fairly easily: What about convergence almost everywhere? That would say that if f is square-integrable, then for "almost every" value of x between 0 and 2π we have This was not proved until 1966 in (Carleson, 1966). For strictly finitary discrete Fourier transforms, these delicate questions of convergence are avoided.
|
So I think my proposed new article is a bit flawed but an improvement on the current situation. Quietbritishjim ( talk) 01:10, 31 December 2012 (UTC)
for the dominated convergence theorem, should'nt it be instead of ?
For we have
so if , this would work as our dominating function. This is true, since