Talk:Functional determinant

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I have added some stuff. There were some things in the article I did not understand (concerning the Lebegue measure), so I did not know where to put them. I removed them, and those who know where they fit can always put them back. MuDavid 15:36, 11 December 2008 (UTC)

Zeta function

In the second paragraph, I recently added the "disambiguation needed" tag to the link to Zeta function, a disambiguation page, but the edit was reverted by MuDavid, saying:

I understand the reason, but not the action: the disambiguation page does not contain any discussion about the general zeta function and, instead, points to numerous irrelevant articles. I couldn't find the correct one from them. Could anyone help, please? — Pt(T) 23:55, 31 January 2010 (UTC)

There is no "correct one", actually. The zeta function being talked about here is the zeta function of the operator the functional determinant is computed of, and each operator has a different zeta function. If the operator has the natural numbers as its spectrum, then we need the Riemann zeta function; if its the natural numbers shifted by a certain constant, then its the Hurwitz zeta function; etc. Unless an article is written specifically about zeta functions connected to operators, I don't think we can point anywhere but to the general article zeta function. MuDavid (talk) 12:50, 1 February 2010 (UTC)
In that case I'd rather prefer a red link drawing attention to the need for yet another zeta function article, like Zeta function (operators). The present link to a disambiguation page needs just as much justification as you have just provided here. What if the spectrum of an operator is empty? Does the operator ${\displaystyle {\hat {A}}(f)(x)=f(x)+1}$ have a zeta function? Precisely what class of operators is needed? It's not obvious that if ${\displaystyle {\hat {S}}}$ is in trace class, then ${\displaystyle {\hat {S}}^{-s}}$ is also, and in what field or ring may the ${\displaystyle s}$ be in?
My main point is, that the subject needs a separate article and if, as it appears, we don't have one yet, then there's enough material to start one, and it is necessary to point our wise readers to the need by rather using a red link. — Pt(T) 14:23, 1 February 2010 (UTC)
Yes, I understand your point. As a physicist, I don't care much about trace classes and existence —I'm happy if I know why it's called "zeta function", and the article zeta function gives me just that. So I'm happier with how it is than I'd be with a red link. But maybe a stub containing what we have already would be better still. I know ample literature exists, but somebody else than me will have to make a synthesis, as I don't know the content of any literature. MuDavid (talk) 13:17, 2 February 2010 (UTC)

Okay, I created zeta function (operator). Let's hope someone expands it... MuDavid (talk) 15:35, 12 March 2010 (UTC)

Mistake

i see one mistake, you are setting sinh(x) instead of sin(x) true solution for the operator

${\displaystyle -D^{2}y(x)+\lambda y(x)=0}$

No, the article as it is now is correct. For positive λ the above equations is solved by sinh(λ x). MuDavid (talk) 10:55, 26 October 2010 (UTC)

Criticism

This article leaves the reader with NO clue why anyone would actually want to compute a functional determinant, or what it is used for.

Also, the examples seem dishonest the way they are worded: they keep promising they are going to show how to compute a determinant but then they never actually compute one - they only compute the ratios between two determinants. Doubledork (talk) 18:33, 2 September 2011 (UTC)

Please go ahead and add the information you feel is lacking. And as for the second comment: the examples compute the determinants up to a multiplicative constant, which is not that dishonest in my opinion. MuDavid (talk) 08:31, 26 September 2014 (UTC)