Talk:De Branges's theorem

[Untitled]
Now a theorem, so a conjecture category could mislead.

Charles Matthews 11:28, 9 Oct 2004 (UTC)

Both cases a0 and a1 are simply consequences of normalization. The case a2 is elementary (originally due to Bieberbach, see Hille's book on analytic functions, vol II, page 350). The first deep case is a3, and was settled by Loewner (then at Stanford, i believe). He sat on the result for a year, hoping that it could be extended. His method is in Ahlfors' little green book on geometric function theory (not the standard Ahlfors' text), and probably in Peter Duren's book and elsewhere. (See also http://mathworld.wolfram.com/BieberbachConjecture.html which has dates.) Schiffer had a big hand in a4 and a5 (the even coefficients are easier, iirc), and i heard him one time remark at a talk that somebody (whose name escapes me) said that the Bieberbach conjecture was perfect for a mathematician, because it was guaranteed employment (you'd do one coefficient at a time, because there would never be a general proof). I believe Schiffer's work used his method of interior variation, instead of Loewner's method of boundary variation. In fact, Loewner's method yields a PDE which in principle could be studied to derive all the coefficients, and that's what de Branges did, in the context of his own theory.

The remark above about Stanford is incorrect. Loewner proved the case n=3 of the Bieberbach conjecture while still in Europe, in 1923. He came to the US in the late thirties, and to Stanford in the fifties. Katzmik 11:28, 26 April 2007 (UTC)

Most popular name?
So the article says it was formerly called the Bieberbach conjecture. I found that odd as I've always thought of it as Bieberbach conjecture, and heard it often referred that way. Do specialists really call it de Branges' theorem? A preliminary look through MathSciNet, seems to indicate that "the de Branges theorem" actually refers to a more general theorem that implies (among other important stuff) the Bieberbach conjecture. --C S (Talk) 07:36, 15 April 2006 (UTC)

FWIW, My complex analysis text book (Arthur David Snider) calls the theorem "De Branges' Theorem". Maybe in the next edition it will be Borcia's theorem :-? —Preceding unsigned comment added by 12.177.23.62 (talk) 23:58, 5 September 2008 (UTC)

Demonstration of non-injectivity in the sufficiency counterexample f(z):=z+z^2
The article states "it is holomorphic on the unit disc and satisfies [...], but it is not injective since f '(-1/2) = 0." Surely this is not complete without also noting f '' (-1/2) > 0, correct? 06:44, 15 May 2006 (UTC)


 * No, you're thinking of real valued functions defined on the real axis. A holomorphic function f defined in the complex plane is injective if and only if its derivative is non-zero. As soon as you have a point z0 with f '(z0) = 0, you know that f cannot be injective near z0. The intuitive reason is that such a function, near z0, has approximately the form g(z) = a + b(z-z0)n for some n&ge;2 (Taylor series), and the function g wraps the circle around z0 n-times around the point a, so is not injective. AxelBoldt 15:14, 16 May 2006 (UTC)

Move?

 * The following discussion is an archived discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section. 

The result of the move request was: Not moved. Jafeluv (talk) 14:32, 12 December 2011 (UTC)

De Branges& → De Branges' theorem –
 * Correct grammar (there shouldn't be an 's' after the apostrophe). Ben (talk) 11:35, 5 December 2011 (UTC)
 * See MOS:POSS – either is acceptable. Jenks24 (talk) 11:39, 5 December 2011 (UTC)
 * Now opposing. As the MoS says, either is acceptable and (a la ENGVAR) we should not move articles between two equally acceptable titles. Jenks24 (talk) 13:15, 11 December 2011 (UTC)


 * Sorry Jenks: that's wrong. MOS (at MOS:POSS) says this, very specifically:
 * Singular nouns
 * For the possessive of most singular nouns, add 's (my daughter's achievement, my niece's wedding, Cortez's men, the boss's wife, Glass's books, Illinois's largest employer, Descartes's philosophy , Verreaux's eagle ). Exception: abstract nouns ending with an /s/ sound, when followed by sake (for goodness' sake, for his conscience' sake).
 * See what I have underlined. The matter is not optional. WP:ENGVAR (also at MOS) says this:
 * (The accepted style of punctuation is covered in the punctuation section, below.)
 * So appeals to ENGVAR in favour of this RM miss the mark. ENGVAR directs us to POSS, which settles on "de Branges's theorem".
 * N oetica Tea? 14:25, 11 December 2011 (UTC)
 * Interesting. Perhaps I've misunderstood the guideline, but I thought that De Branges's theorem would fall under the second bullet point:
 * For the possessive of singular nouns ending with just one s (sounded as /s/ or /z/), there are three practices:
 * Add 's: James's house, Sam Hodges's son, Jan Hus's life, Vilnius's location, Brahms's music, Dickens's novels, Morris's works, the bus's old route.
 * Add just an apostrophe: James' house, Sam Hodges' son, Jan Hus' life, Vilnius' location, Brahms' music, Dickens' novels, Morris' works, the bus' old route.
 * Add either 's or just an apostrophe, according to how the possessive is pronounced:
 * Add only an apostrophe if the possessive is pronounced the same way as the non-possessive name: Sam Hodges' son, Moses' leadership;
 * Add 's if the possessive has an additional at the end: Jan Hus's life, Morris's works.
 * Some possessives have two possible pronunciations: James's house or James' house, Brahms's music or Brahms' music, Vilnius's location or Vilnius' location, Dickens's novels or Dickens' novels.
 * My reading of that is that we can use either De Branges's theorem or De Branges' theorem, as long as we use one consistently (or have I misunderstood how De Branges is pronounced?). By the way, I was not trying to say this is an ENGVAR issue – rather, that it is similar to ENGVAR in that we pick one style and stick with it consistently throughout the article. Anyway, happy to be proven wrong, either way the article should be at the current title. Jenks24 (talk) 15:32, 11 December 2011 (UTC)
 * What you excerpt is not the applicable section, Jenks. Our case does not have an "s" that is pronounced, "sounded as /s/ or /z/". It is as silent as each "s" in "Descartes". Anyway, good to see that you have now changed your mind. N oetica Tea? 03:42, 12 December 2011 (UTC)
 * Sorry to be a pain, but can you verify that statement? Having a quick google, I found this and this, which give the pronunciation as "deh-BRAHNZH" and "de-BRÄNZH" respectively. I must admit this is not my strong suit (I don't know IPA and so on), but doesn't that mean that the s is sounded as a /z/? Jenks24 (talk) 10:41, 12 December 2011 (UTC)
 * Sure I can verify it, Jenks. The sounds /z/ (as in "zoo") and /ʒ/ (as in "pleasure" and "beige"; often represented informally as /zh/) are quite distinct in both English and French. The MOS guideline uses /s/ and /z/ with precision: /s/ is sometimes spelt with "c[e,i,y]", and the "s" of interest at the end of a word is often sounded as /z/ ("bees", "beds", "bugs", but not "bucks"). The distinctions have to be made accurately, even if some people are unaware of the IPA niceties, or unaware of the facts of their own speech (and we all have a foot in that camp).
 * I hope that helps. Take it to my talkpage if you want more (though I'm completely busy in the world just now). I agree with Dick that some things need fixing with MP:POSS (see below; I tried hard, a couple of years back). But those linguistic facts are accurate, I assure you.
 * N oetica Tea? 12:46, 12 December 2011 (UTC)
 * Thanks for the clarification, Noetica. I now agree that it is the first section, not the second, of MOS:POSS that we should apply here. Cheers, Jenks24 (talk) 13:12, 12 December 2011 (UTC)


 * Oppose – nom needs to learn grammar before asserting wrongly. Dicklyon (talk) 07:15, 7 December 2011 (UTC)
 * I did not know that either was acceptable, but can you please explain why I was explicitly wrong? Ben (talk) 08:15, 7 December 2011 (UTC)
 * I guess Dicklyon wanted to say that "de Branges" is a French name, therefore the "s" is not pronounced. Therefore the rule of MOS:POSS does not apply (it is only stated for nouns that end with an /s/ or /z/ sound). Sasha (talk) 15:43, 7 December 2011 (UTC)
 * Incorrect, Sasha. See the excerpt of MOS:POSS that I have posted, above. N oetica Tea? 14:25, 11 December 2011 (UTC)


 * Whether it's French or pronounced or not, it is incorrect to assert that "there shouldn't be an 's' after the apostrophe". If it is in fact French and the s is silent, then that s is not even optional.  I've been through such exercises enough to be easily annoyed; sorry about that.  Dicklyon (talk) 16:07, 7 December 2011 (UTC)
 * Unless I'm reading the apostrophe article incorrectly, it disagrees with you. Admittedly I was taught to leave off the extra  's'  and I did not know that either was acceptable, which lead me to filing this RM. Given that either is acceptable acceptable I'm not really worried about which way this RM goes now, although my preference is still for de Branges' theorem because that's what I'm comfortable with. Cheers, Ben (talk) 21:35, 7 December 2011 (UTC)
 * Indeed, Apostrophe is also ambiguous also allows both practices. Sasha (talk) 00:43, 8 December 2011 (UTC)
 * Ambiguous? How? It describes both practices, doesn't it? "The English possessive of French nouns ending in a silent s, x, or z is rendered differently by different authorities." And so on. N oetica Tea? 02:46, 8 December 2011 (UTC)
 * I think he means that it doesn't support my assertion that the s is not optional. Perhaps I'll learn something here myself.  But not from an unsourced claim in a WP article; what do guides say about this?  This one supports what I always thought.  Dicklyon (talk) 03:17, 8 December 2011 (UTC)
 * too complicated for a non-native speaker like me :( Even Oxford and Longman do not quite agree on this. Sasha (talk) 05:39, 8 December 2011 (UTC)
 * I don't see either of them discussing this case. But advice does vary on the s after apostrophe.  Dicklyon (talk) 06:03, 8 December 2011 (UTC)
 * But MOS:POSS makes a clear ruling, and it is exactly the resource to be using here. N oetica Tea? 14:25, 11 December 2011 (UTC)


 * Oppose. Neither Apostrophe nor WP:MOS is against addition of that "s", and WP:MOS is against omission of that "s" . As a major contributor to both those pages, I have researched the matter minutely. I have surveyed many style guides and related resources. My own preference is to add the "s", and this is strongly supported in the guides and in best-practice publishing. N oetica Tea? 02:46, 8 December 2011 (UTC)
 * Oppose (per the discussion above). Sasha (talk) 03:04, 8 December 2011 (UTC) Let me summarise what I understood from it:
 * de Branges has a silent s (like Descartes). Perhaps we should add the phonetic transcription ([də bʁɑ̃ŋʒ] or something like that) to the article.
 * WP:MOS prescribes de Branges's theorem in this case.
 * Apostrophe allows both de Branges' theorem and de Branges's theorem.
 * WP:ENGVAR links to both WP:MOS (in bullet 4) and Apostrophe (in bullet 5), so it is not of great help.
 * At least some of the detailed manuals (e.g. the one of Dicklyon) prescribe de Branges's theorem, but the manuals are not very consistent (in particular, it seems that the rules have become more flexible in the 1960's).
 * Summary: de Branges's theorem is at least as good as de Branges' theorem, therefore there is no reason to move it.
 * Sasha (talk) 15:44, 11 December 2011 (UTC)
 * Sasha, ENGVAR does not link to Apostrophe. It clearly excludes punctuation from its own scope, and defers to MOS:POSS (via MOS:PUNCT).
 * Summary (and I invite you to correct your own): Both forms are used in the literature, because this is a style matter par excellence; Wikipedia's own style (see WP:MOS) consistently and definitely calls for "de Branges's theorem". The ENGVAR component of WP:MOS has no bearing on the present case.
 * N oetica Tea? 03:42, 12 December 2011 (UTC)
 * Sasha, here is the complete text of WP:ENGVAR:
 * {| class="collapsible collapsed" style="width:100%;font-size:88%;text-align: left; border: 0px; margin-top: 0.2em;"

! style="background-color: #aaffaa;" | Complete text of WP:ENGVAR
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 * }
 * Please indulge me, Sasha. Show me, by underlining if you like, where this section of WP:MOS called WP:ENGVAR "links to both WP:MOS (in bullet 4) and Apostrophe (in bullet 5)". I'm not seeing it.
 * N oetica Tea? 05:35, 12 December 2011 (UTC)


 * Support. This is properly a style issue rather than a Googling issue. But it seems that the style guides fail to clarify the matter. I get 280 post-1980 English-language Google Book results for "De Branges' theorem", 25 for "De Branges's theorem". Wolfram's MathWorld uses "de Branges' proof." Kauffner (talk) 05:33, 9 December 2011 (UTC)
 * note that some of the 280 results are for "the de Branges theorem" without a possessive apostrophe. But this is strange indeed. Sasha (talk) 15:27, 9 December 2011 (UTC)
 * Kauffner, if it's a style issue, and you want to appeal to style resources, why do you not go straight to WP:MOS? It calls for "de Branges's theorem". If you want that changed, go to WT:MOS and talk about it. This business of appealing to MOS when it suits one's own opinion, ignoring it in all other cases, is an abuse. N oetica Tea? 14:25, 11 December 2011 (UTC)
 * You must know better than this. The MOS lists all the possibilities and doesn't recommend anything. Kauffner (talk) 05:02, 12 December 2011 (UTC)
 * An absurdity. MOS is replete with recommendations. You must know nothing about MOS. I, on the other hand, am renowned as a MOS specialist (if I have any slight claim to fame at all). Read MOS, rather than simply appealing to it captiously when doing so appears to suit your pre-formed opinion. N oetica Tea? 05:44, 12 December 2011 (UTC)
 * Actually, Noetica, the MOS does have a severe lack of guidance in MOS:POSS in the bullet "For the possessive of singular nouns ending with just one s (sounded as /s/ or /z/)". And one might think this case is applicable here, depending on how one thinks the guy's name is pronounced.  But the other bullet point does have a good strong recommendation, which seems to me is more applicable here.  It's well illustrated with words ending in /s/, which helps.  It would be nice if we could add some better recommendation to that other mess; we all recognize that authoritative opinions vary, but that doesn't mean we can't at least pick a style that's pretty broadly acceptable and recommend it.  In practice, I think the third option is the only one that's close to what most people do, and pretty broadly supported, though some guides get more specific, e.g. on monosyllabic vs otherwise.  Dicklyon (talk) 05:56, 12 December 2011 (UTC)
 * The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.

comment on previous discussion
Noetica is right, I am wrong, so future readers, please ignore my item #4. Sasha (talk) 15:11, 12 December 2011 (UTC)