Talk:Function of several complex variables/Archive 1

Vote for new external link

Here's my website full of example problems from complex variables. Someone please put it in the external links section if you think it's helpful!

http://www.exampleproblems.com/wiki/index.php/Complex_Variables

Not relevant, the link is about 1 variable, not several, like this article. Oleg Alexandrov (talk) 02:47, 29 December 2005 (UTC)

Agree with Oleg — not relevant. - Gauge 00:23, 8 January 2006 (UTC)

When several complex people agree on the same thing, it must be true! :) Oleg Alexandrov (talk) 02:32, 8 January 2006 (UTC)

Deformations of complex structures

On the sixth paragraph (the one that starts "from this points onwards there was a foundational theory...") mentions deformation theory of complex structures. Why is this on the foundations of the theory? I would find it quite interesting if a reason for the study of deformations of complex structures was given - and why it is considered to be one of the pillars (foundations) of the subject.

I would also find it quite nice if some applications of several complex variables to PDEs were mentioned.

I think that if this, quite nice, entry on several complex variables would include these two things, it would become even more enlightening. — Preceding unsigned comment added by 155.198.157.113 (talk • contribs) 18:57, 21 July 2006

Typesetting reversion

I reverted since there was an inconsistent mixture of typography: LaTeX and {{bigmath}}/{{math}} for inline and displayed formulae. The IP cleaned up the mixture. I'll check in detail if there were any typos the IP introduced in his/her edit, which may have motivated this reversion by Incnis Mrsi. M∧Ŝc²ħεИ_τlk 14:01, 17 June 2013 (UTC)

Could you look for IP’s user_talk before igniting an edit war? I reverted and will revert unconditionally an illegible crap like “−I”. The “imaginary unit i” also looks ugly, although I would not revert it were this one the only degradation. BTW, I do not see anything bad with “LaTeX and {{bigmath}}/{{math}} mixture of typography”: the purpose of {{math}} is namely to match appearance of <math> more closely than wiki code does. Incnis Mrsi (talk) 14:48, 17 June 2013 (UTC)

But the fonts in {{math}} are still different to LaTeX and people think it's jarring. I anticipated you'd say all this. Which is why, if there are no edit conflicts, I'll insert {{math}} uniformly inline leaving LaTeX displayed. M∧Ŝc²ħεИ_τlk 14:53, 17 June 2013 (UTC)

Also, consult WP:MOSMATH #Blackboard bold please. There are plenty of article where formatting is really poor. Why people like you and 99.241.86.114 start quarrels over typesetting preferences in relatively clean articles? Incnis Mrsi (talk) 14:59, 17 June 2013 (UTC)

I don't want to start an edit war, nor quarrel over my own preferences, just trying to to clean up the silly mix is all. You say this is a "relatively clean" article when LaTeX, HTML, and WP templates are used all over the place (LaTeX is inline and {{math}} displayed). As for the pointer to WP:MOSMATH, the article has a mix of Cⁿ and $\mathbb {C} ^{n}$, so tried to make them all consistent as blackboard bold - if others insist they could all be changed to bold after. M∧Ŝc²ħεИ_τlk 15:06, 17 June 2013 (UTC)

I do not obstruct any change which unambiguously improves at least something and does not make any demonstrable harm to the rest of code. Incnis Mrsi (talk) 15:16, 17 June 2013 (UTC)

I tried again in this edit, and assumed bold was the preference instead of blackboard bold for the real and complex number sets . M∧Ŝc²ħεИ_τlk 10:36, 18 June 2013 (UTC)

Too technical

I hope it's OK that I added the "technical" template at the top of the article. The reason is that the article doesn't give an overview that's comprehensible to someone who isn't already quite familiar with the subject. The lead is fine, but the next paragraph assumes intimate familiarity with the subject. The article could really do with a first section that introduces the subject to someone who's familiar with the prerequisites (e.g. single-variable complex analysis, multivariable real calculus) but who hasn't studied multivariable calculus per se. (Unfortunately I cannot write such a section, as I am a member of this target audience.) Nathaniel Virgo (talk) 13:05, 3 January 2015 (UTC)

You need to be still more specific. The paragraph following the lead is in the history section. Such a section is not even intended to be understood mathematically (for those unfamiliar with the subject). The section after that is on ℂⁿ. Is it here you get stuck? YohanN7 (talk) 16:40, 3 January 2015 (UTC)

I've moved the paragraph "The Cⁿ space" to the last, because it brings an example of Stein manifold but it needs a lots of efforts to reach it. Cousin problem, Levi problem, and the development of several complex variables must be explained, I think.--Enyokoyama (talk) 10:00, 23 March 2015 (UTC)

Assessment comment

The comment(s) below were originally left at Talk:Function of several complex variables/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

Needs splitting into sections, comparisons with single-variable case, examples, why they are "supposed to be" analytic, etc. Tompw 13:29, 20 November 2006 (UTC)

Last edited at 12:08, 16 April 2007 (UTC). Substituted at 02:35, 5 May 2016 (UTC)

Fix the ambiguous use of "these" and "they"

If the intended meaning of the first paragrah is that the theory of several complex variables studies only holomorphic functions then first sentence in the paragraph should say so. As the current article stands, the first sentence speaks of complex valued functions on complex n-tuples. The next sentence in the article says that "these functions" are "not just any functions". It is unclear which functions "these functions" refers to.

It would be clearer if the article began: "The theory of several complex variables deals with with a special type of complex valued functions on n-tuples of complex numbers. The functions of this special type are the holomorphic functions." - if that is the intended meaning.

Tashiro~enwiki (talk) 07:38, 23 June 2016 (UTC)

Series name

Considering the relationship with Cauchy's integral formula, I think it is good to use the page of Laurent expansion for explanation, but since it is a holomorphic point, I would like to describe it as Taylor expansion, Is there a good way?--SilverMatsu (talk) 12:53, 7 November 2020 (UTC)