Talk:Fourier inversion theorem

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)

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)

Reference?

When discussing the Fourier inversion for L¹ functions we have the statement

In such a case, the integral in the Fourier inversion theorem above must be taken to be an improper integral (Cauchy principal value)

$\lim _{b\rightarrow \infty }{\frac {1}{2\pi }}\int _{-b}^{b}({\mathcal {F}}f)(t)e^{itx}\,dt$

rather than a Lebesgue integral.

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)

article needs explanation of the general case for a locally compact group

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)

proof

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)

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 will probably follow, 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)