Talk:Prolate spheroidal wave function

Mathematics Start‑class Low‑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
Start	This article has been rated as Start-class on Wikipedia's content assessment scale.
Low	This article has been rated as Low-priority on the project's priority scale.

Articles for creation Start‑class

	This article was reviewed by member(s) of WikiProject Articles for creation. The project works to allow users to contribute quality articles and media files to the encyclopedia and track their progress as they are developed. To participate, please visit the project page for more information.Articles for creationWikipedia:WikiProject Articles for creationTemplate:WikiProject Articles for creationAfC
Start	This article has been rated as Start-class on Wikipedia's content assessment scale.
	This article was accepted on 17 September 2007 by reviewer Graeme Bartlett (talk · contribs).

Revision required

Contrary to what the first paragraph claims, the PSWFs are not time-limited. If $\psi _{n}$ were in fact time-limited, the second $Q_{T}$ in the expression $Q_{T}P_{W}Q_{T}\psi _{n}=\lambda _{n}\psi _{n}$ would be redundant anyway. Based on the original paper by Slepian and Pollack, and using the notation established in this article, the correct expression seems to be

P_{W}Q_{T}\psi _{n}=\lambda _{n}\psi _{n}

where $\psi _{n}$ are bandlimited. Perhaps somebody with more background in this matter can confirm this. Qopzm (talk) 00:39, 8 July 2010 (UTC)[reply]

I agree

I agree with this observation, that the PSWF's are not time limited. In fact, they are defined to be those functions which maximise the power contained the region [-T,T] given the constraint that they have unit power on R. I have constructed explicitly these functions and they do not vanish outside a compact interval. Indeed, it is a general result that a function which vanishes on a compact interval necessarily cannot have a frequency content which vanished on a compact interval. I will work on the revision to this incorrect material. angusprain 18:25, 1 March 2013.