Re: Dense subspace of L2 (R)
- From: José Carlos Santos <jcsantos@xxxxxxxx>
- Date: Sat, 01 Aug 2009 01:44:11 +0100
On 31-07-2009 21:55, Gauster wrote:
What's the easiest way to prove that the functions x^n.e^(-x^2/2)
span a subspace that is dense in L2 (R) ?
I don't know if this is the easiest way, but it is not hard to prove
that, for each continuous function _f_ from R into R with compact
support and for each r > 0, there is a linear combination _g_ of
functions of the form x^n.e^(-x^2/2) such that ||f - g||_2 < r. Since
the set of continuous function from R into R with compact support is
dense in L^2(R), this is enough.
Best regards,
Jose Carlos Santos
.
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