Talk:Dirac delta function

Skip to table of contents

This is the talk page for discussing improvements to the Dirac delta function article.
This is not a forum for general discussion of the article's subject.

Put new text under old text. Click here to start a new topic.
New to Wikipedia? Welcome! Learn to edit; get help.

Article policies

Find sources: Google (books · news · scholar · free images · WP refs) · FENS · JSTOR · TWL

Archives: Index, 1, 2: 6 months

Dirac delta function has been listed as one of the Mathematics good articles under the good article criteria. If you can improve it further, please do so. If it no longer meets these criteria, you can reassess it.

Article milestones
Date	Process	Result
September 29, 2010	Good article nominee	Not listed
October 1, 2010	Good article nominee	Listed

Current status: Good article

Mathematics High‑priority

	Mathematics portal This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics
High	This article has been rated as High-priority on the project's priority scale.

Engineering High‑importance

	Engineering portal This article is within the scope of WikiProject Engineering, a collaborative effort to improve the coverage of engineering on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.EngineeringWikipedia:WikiProject EngineeringTemplate:WikiProject EngineeringEngineering
High	This article has been rated as High-importance on the project's importance scale.

Physics High‑importance

	Physics portal This article is within the scope of WikiProject Physics, a collaborative effort to improve the coverage of Physics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.PhysicsWikipedia:WikiProject PhysicsTemplate:WikiProject Physicsphysics
High	This article has been rated as High-importance on the project's importance scale.

Archives

Index 1, 2

This page has archives. Sections older than 180 days may be automatically archived by when more than 4 sections are present.

Proposal: change name from Dirac delta function to Dirac delta distribution

I suggest to rename the mathematical object and the page "Dirac delta distribution". Although using the word function is common, it is also common to call it distribution, which is more appropriate mathematically. Skater00 (talk) 16:35, 21 March 2024 (UTC)[reply]

I think WP:COMMONNAME favors the current "Dirac delta function". I will add another reason for keeping things as they are: prospective readers of the article will all have heard of "function", but not know "distribution", and may as a result be uncertain whether they have arrived at the correct article. Thus the current naming is the least likely to cause confusion. Tito Omburo (talk) 09:10, 22 March 2024 (UTC)[reply]

I will agree with Tito because we start by clarifying that there is no function having this property. As long as the scare quotes remain, our opening paragraph immediately corrects laypeople new to the topic. Skater is of course right, and that is why the clarification belongs in the introduction, and why my support is conditional on that.

It might still be best to improve the rest of the article, though K Smeltz (talk) 21:50, 25 August 2024 (UTC)[reply]

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)[reply]

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)[reply]

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)[reply]

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)[reply]

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)[reply]

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