- in a way Fourier series is a discrete analogy, in that it maps to a discrete span of functions. --anon
(Disclaimer: I am not a native english speaker, so the following remark might be false.) One can find the word "integral transform" as well as "integral transformation" in the literature. I tried to figure out the appropriate meanings with the following result: These words should be used as in "The Laplace transformation L associates to a function f its Laplace transform Lf". If this is correct, the page should be adjusted. Th. Bliem. --18.104.22.168 08:57, 17 October 2005 (UTC)
I find the section on orthogonality to be useless or incorrect. It speaks of basis functions, which are undefined and not obviously related at all to general integral transforms. It refers to the kronecker delta, when I think it means dirac; but it would still be wrong because it should be delta(y-5)*delta(x-3) - not any scaling. If people agree, we should just get rid of it.
- I agree, it is worded incorrectly, I have updated it.Jackminardi (talk) 09:53, 25 December 2011 (UTC)
I never knew that the basis functions of integral transforms had to be orthogonal, can you give a reference? How are the basis functions of the Laplace transform orthogonal? Classwarz (talk) 10:28, 24 January 2012 (UTC)
Helpful for a layperson
I found the exposition here extremely clear, and the links very helpful. It gave me context I needed for digital signal processing without overwhelming me with the mathematics.
Dana Good 22.214.171.124 16:18, 28 March 2007 (UTC)
I don't pretend to be an expert on this subject, but in "A symmetric kernel is one that is unchanged when the two variables are permuted." couldn't 'permuted' be changed to 'swapped', or something else implying that their order doesn't matter? Using the word permuted seems a little excessive when there's only two possible permutations. I may be misinterpreting this, of course (in which case the sentence should probably be clarified!) --Jonnty (talk) 07:09, 27 December 2009 (UTC)
I have added the wavelet transform to the list, nevertheless I am not a real expert and am not entirly sure this is mathematically a intergral transfomr, nevertheless would appriciate input from someone with better knowledge. I ' have added it because I think it had to be added to be more complete. —Preceding unsigned comment added by 126.96.36.199 (talk) 13:21, 4 January 2010 (UTC)
The link Integral operator redirects to this entry, but integral transforms are only very particular integral operators: integral operators are simply maps between function spaces defined by means of a integral of one or more dimension. An ideal entry about integral operators should describe the ideas of Vito Volterra, Ivar Fredholm and necessarily describe also nonlinear operators (note the irony of this last redirected link :D ). --Daniele.tampieri (talk) 19:50, 5 June 2010 (UTC)
Rubik's Cube Analogy
This stuff is pretty abstract, but there is a simple, very visual analogy to so-called setup moves on Rubik's cube. For example, there is a simple algorithm for switching two sets of two cublets in the Rubik's cube, but it only works if the cublets are in the right place. So you use a setup move that moves the cublets to the (relative) positions, execute the algorithm, and "undo" the setup moves to get the desired result.
Should it not be instead of ?
The transform takes the function f, which is a function of t, and transforms it to T(f), which is a function of u. So it should be T(f)(u). Right?