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WikiProject Mathematics (Rated C-class)
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A comment to note 14: It is not true that Hörmander did not define f(t) on the whole real line, since otherwise it would be a mistake to consider f(1 - |x|^2) because the argument is not always positive for x in R^n. Also it is not clear who \varphi_2 is under "Smooth cutoff functions". Maybe an edit of the wiki page can improve the article. — Preceding unsigned comment added by (talk) 07:28, 21 May 2013 (UTC)

Oleg, thanks for correcting my silly mistake. I must have been really tired. - Gauge 04:57, 16 January 2006 (UTC)

You're welcome! :) It does look look confusing, if you expect something like
e^{-x^2}. :) Oleg Alexandrov (talk) 07:09, 16 January 2006 (UTC)
should we change it to exp( -1 / (1 - x² )) ? — MFH:Talk 23:46, 30 March 2006 (UTC)

In the end, it says you can create a smooth cutoff funtion from any set, but this is of course, not true. The set must be compact, otherwise what is this "distance from the set"...


The intro touches on applications of mollifiers: to create a sequence of smooth functions approximating a nonsmooth one. It doesn't go into much detail, though. Could someone add some example applications? Also, this seems closely related to scale space, although that uses a Gaussian kernel which doesn't have compact support. —Ben FrantzDale (talk) 01:53, 29 May 2008 (UTC)