Compact support of a function

  • Thread starter mnb96
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  • #1
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Hello,
given a function f:R->R, can anyone explain what is meant when we say that "f has compact support"?

Some sources seem to suggest that it means that f is non-zero only on a closed subset of R.
Other sources say that f vanishes at infinity. This definition seem to contradict the previous: for example the Gaussian is never 0 but does vanish at infinity.

So, where is the misunderstanding?
 

Answers and Replies

  • #2
mathman
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Compact support means the function is zero everywhere outside some finite interval. Gaussian does not have compact support.
 
Last edited:
  • #3
disregardthat
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It naturally means that the support of the function is a compact set, or equivalently as mathman points out; contained in a finite closed interval. This implies that f must vanish at positive and negative infinity, but is not equivalent as your example shows.
 

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