Wikipedia:Articles for deletion/Cheung–Marks theorem


 * The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review).  No further edits should be made to this page.

The result was   no consensus. Shimeru (talk) 00:03, 31 May 2010 (UTC)

Cheung–Marks theorem

 * – ( View AfD View log  •  )
 * Believe to be a non-notable mathematical theorem; at least to the extent of not requiring a Wiki article. The original paper has very few citations, and Google only returns a small handful of relevant hits for "Cheung–Marks".

Was originally PRODded; removed by article's author. Oli Filth(talk&#124;contribs) 11:05, 15 May 2010 (UTC)
 * Weak Delete&mdash;Unfortunately it doesn't appear to satisfy the necessary criteria for notability.&mdash;RJH (talk) 18:03, 16 May 2010 (UTC)
 * Keep. From update, this looks to be a correction to the only error Shannon's 1948 Bell Labs paper that founded information theory.BigChairMonk (talk) 19:49, 19 May 2010 (UTC) — BigChairMonk (talk • contribs) has made few or no other edits outside this topic.


 * That's not important (and not correct, either!). What's important is whether the theorem has been discussed in a non-trivial manner in multiple independent sources, e.g. textbooks.  Oli Filth(talk&#124;contribs) 19:53, 19 May 2010 (UTC)
 * Keep I had a class with Makrs and got an account just to vote on this. Bob Koffee —Preceding unsigned comment added by BobKoffee (talk • contribs) 19:28, 20 May 2010 (UTC)   — BobKoffee (talk • contribs) has made few or no other edits outside this topic.
 * This isn't a vote! It's a discussion on reasons to keep or delete the article.  Oli Filth(talk&#124;contribs) 11:23, 21 May 2010 (UTC)


 * Keep. Here are some references from varying perspectives.


 * "Coined". Brown, J.L., Jr.; Cabrera, S.D.;, "On well-posedness of the Papoulis generalized sampling expansion , " Circuits and Systems, IEEE Transactions on , vol.38, no.5, pp.554-556, May 1991. Brown and Cabrera coined the term term "Marks-Cheung Theorem" based on the original paper. From abstract - "K.F. Cheung and R.J. Marks  have shown that if at least one of the interpolation functions used in the generalized sampling expansion of A. Papoulis (1977) is not square-integrable, then the problem is ill-posed in the sense that the variance of the reconstruction error is unbounded when noisy samples are used." and, from the paper, "the Cheung-Marks theorem needs to be restated in terms of the (YJw)); an alternative proof  shows that the problem is well posed only when each of the {Yk(w)} belongs to L2( - a, a). This latter result, along with a more detailed proof of Theorem 1, can be found."


 * Historical. Unser, M.;, "Sampling-50 years after Shannon," Proceedings of the IEEE , vol.88, no.4, pp.569-587, Apr 2000. Unser Cited Cheung-Marks paper in the most important developments of the sampling theorem in the last 50 years.


 * In Practice . While et al. Generalized sampling interpolation of noisy gravity/gravity gradient data. GEOPHYSICAL JOURNAL INTERNATIONAL   Volume: 178    Issue: 2    pp  638-650    AUG 2009 (1985); Reference Marks & Cheung. "It is shown that the GSE is well-posed if 0 < | det[H(k)]| < 8, where H is the expansion matrix (described below in eq. 1), and k is the wavevector..."


 * Generalization to vector sampling. Seidner, D.; Feder, M.;, "Vector sampling expansion," Signal Processing, IEEE Transactions on , vol.48, no.5, pp.1401-1416, May 2000: "The first issue is well posedness. In GSE, this problem was initially discussed by Cheung and Marks [17], who found a sufficient condition for ill-posedness of the system. Under their definition, an ill-posed GSE system produces a reconstruction error with unbounded variance when a bounded variance noise is added to the samples."

 Please add new comments below this notice. Thanks, Black Kite (t) (c) 22:07, 23 May 2010 (UTC)
 * Frame Sampling.The Journal of Fourier Analysis and Applications Volume 2, Number 5, 1996 Frame Analysis of Irregular Periodic Sampling of Signals and Their Derivatives M. Zibulski, V. A. Segalescu, N. Cohen, and Y. Y. Zeevi: Reference Marks & Cheung. "...in such a case reconstruction might be possible with troublesome convergence properties (which is the reason for calling the sampling unstable)."
 * — SlimDeli (talk • contribs) has made few or no other edits outside this topic.
 * The existence of these one-sentence (or less, for example the "Sampling-50 years after Shannon" paper doesn't even mention Cheung-Marks, merely one cite amongst three) mentions would merit, at most, a footnote in the sampling theorem article. A full-blown article is unwarranted given that the term "Cheung-Marks theorem" is essentially unheard of.  Oli Filth(talk&#124;contribs) 00:52, 22 May 2010 (UTC)
 * Relisted to generate a more thorough discussion so consensus may be reached.


 * I think it's inappropriate that this article was nominated for deletion so quickly. A stub was created, and then the article was proposed for deletion within an hour, with no discussion on the discussion page.  Sometimes you can tell from the initial stub that something is original research, but that doesn't seem to be the case here.  Sure, in the long run the subject needs to prove its notability, but I have seen topics that were clearly crazy treated more gently than this one.  -- Walt Pohl (talk) 11:14, 25 May 2010 (UTC)
 * For reference, I originally PRODded this, because it wouldn't meet CSD. The author removed the tag, so I AfDed it instead.  I don't believe this to be original research, I simply believe it's a theorem with very little exposure.  Actually, there was some discussion on the talk page, but that's orthogonal to whether an AfD should take place (which in itself is a discussion!).  Oli Filth(talk&#124;contribs) 12:00, 25 May 2010 (UTC)
 * Well, I'm rather foreign to informatics (and to English wiki notability rules as well), but: a quick google search, in addition to what was mentioned above, gives, for instance, Brown, J.L., Jr. Cabrera, S.D., Multi-channel signal reconstruction using noisy samples, that mentions their result in the abstract: ''...proving a converse to the ill-posedness result K.F. Cheung and R.J. Marks...".
 * So it seems to me that we indeed can conclude that not only the result exists, but also that it is still of interest to (some) people, that the notability conditions (at least as far as I can see), are met. The result is mentioned in other papers, other researchers are generalizing it, proving the converse statement, etc. For instance, given the abstract of this paper, it means that some part of the paper (seemingly independent from Cheung and Marks themselves) is devoted to things around this result. So it interests some people.
 * Well, that's more or less all I can say after a quick googling. To say more -- maybe one should read these papers through... --Burivykh (talk) 21:55, 25 May 2010 (UTC)
 * The original paper has citations. Keep.  --SmokeyJoe (talk) 12:06, 30 May 2010 (UTC)
 * The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.