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)