Talk:Dirac delta function

complex analysis

This also comes up in complex harmonic analysis, right? Is there a corresponding theory of generalized functions in C? It doesn't like it can be done the same way as in the reals. 03:29, 1 May 2024 (UTC) 2601:644:8501:AAF0:0:0:0:6CE6 (talk) 03:29, 1 May 2024 (UTC)

For Banach spaces of holomorphic functions, it is usually the case that evaluation at a point is a continuous linear functional, that is, an ordinary element of the dual space. For example, Hilbert spaces of holomorphic functions are reproducing kernel Hilbert space, the most basic example of which is the Bergman kernel, which in some sense represents the "Dirac delta" in this situation. Tito Omburo (talk) 00:55, 27 August 2024 (UTC)

Time-delayed Dirac delta

Dirac_delta_function#As_a_measure and Dirac_delta_function#Resolutions_of_the_identity

appear to disagree with Dirac_delta_function#Translation

The result is used at Uncertainty_principle#Proof_of_the_Kennard_inequality_using_wave_mechanics ;ones 7->8 Darcourse (talk) 16:58, 26 December 2024 (UTC)

Missing source

@CaseAsCasy The text has a citation to Kanwal 1983, p. 53-54 but there is no Kanwal in the refs. The closest I found is

• Kanwal, R. P. (2012). Generalized functions: theory and applications. Springer Science & Business Media.

which has CHAPTER 3 "Additional Properties of Distributions 3.1. Transformation Properties of the Delta Distribution" with formula similar to the content but with only a single root. Johnjbarton (talk) 05:23, 25 January 2025 (UTC)

The inline citation makes no sense indeed. But if you combine

Kanwal - 2004 - Generalized Functions pp.50-51

with

Gelfand & Shilov 1966–1968, Vol. 1, §II.2.5

cited in Dirac_delta_function#Composition_with_a_function, then you might be able to derive the expression.

However, I think the edit should be reverted. It's not referenced, $g(x)$ is not defined and the statement lacks context.

Furthermore, simply changing the reference to Kanwal and/or Gelfand would not suffice, as the editor claims the "formula in the citation is not correct".

Kind regards, Roffaduft (talk) 06:54, 25 January 2025 (UTC)

I agree and reverted for now. Johnjbarton (talk) 17:09, 25 January 2025 (UTC)

The reference is the same textbook, different version, not sure how to properly add this. By the way, 2012 edition does not exist, 2004 is the latest one. The context is similar formula for \delta(g(x)) in the section Composition with a function (where the definition for g(x) is implied from lhs, maybe here should also mention smoothness). Generalization for multiple roots is trivial. CaseAsCasy (talk) 23:51, 26 January 2025 (UTC)

not sure how to properly add this

Verifiability is one of wikipedia's core content policies, not an afterthought. I strongly recommend reading up on how to properly cite sources, i.e., how to add a reference and inline citation (personally, I like to use https://citer.toolforge.org/).

Generalization for multiple roots is trivial

Making assumptions on the triviality is usually not a good starting point. In this case, the generalization is not immediately clear from the rest of the article or the reference.

I think these are the most important issues. If these are addressed, then we can talk about the lack of context (e.g. defining $g(x)$).

Kind regards, Roffaduft (talk) 08:07, 27 January 2025 (UTC)

Article review

It has been a while since this has been reviewed, so I took a look and noticed the following:

• The GA review consisted of a checkmark, and did not include any details on what checks were conducted. While today's extensive reviews might not have been necessary back then, I think a little bit more information was still necessary. Other reviewers might want to spotcheck the article against the criteria.
• There is a lot of uncited text. Some uncited statements are covered under WP:CALC. Other statements such as the following do need citations (and I can add other "citation needed" templates if requested:

• "The Dirac delta is used to model a tall narrow spike function (an impulse), and other similar abstractions such as a point charge, point mass or electron point"
• "In applied mathematics, as we have done here, the delta function is often manipulated as a kind of limit (a weak limit) of a sequence of functions, each member of which has a tall spike at the origin"
• "In probability theory and statistics, the Dirac delta function is often used to represent a discrete distribution, or a partially discrete, partially continuous distribution, using a probability density function (which is normally used to represent absolutely continuous distributions)." do need citations to verify this information.

• There is POV and opinionated language in the article, such as "Unfortunately, the actual limit of the functions (in the sense of pointwise convergence) is zero everywhere" (Why is this unfortunate?) and "Although using the Fourier transform, it is easy to see that this generates a semigroup in some sense" (it may not be easy for the reader to see). These were found in a quick skim: I think the entire article might need a copyedit to ensure that POV languauge is removed.

Should this article go to WP:GAR? Z1720 (talk) 01:14, 29 June 2025 (UTC)

@Z1720 Sorry but can you please wait until Matrix (mathematics) and Addition are completely improved? Some users may not have the time to improve it. Dedhert.Jr (talk) 11:04, 29 June 2025 (UTC)

• @Dedhert.Jr: Happy to wait! If editors offer to improve an article, I won't send it to GAR. Z1720 (talk) 14:12, 29 June 2025 (UTC)

If you want to tag some things, I'm happy to work on it if I have the time. Tito Omburo (talk) 18:04, 29 June 2025 (UTC)

@Tito Omburo: I added some citation needed tags per the request above. I probably did not get them all, so if you find a citation to put somewhere, I recommend it. Z1720 (talk) 18:22, 29 June 2025 (UTC)

Thanks! Tito Omburo (talk) 21:10, 29 June 2025 (UTC)