Talk:Mollifier

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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 89.162.87.196 (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"...

Applications[edit]

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)