Timeline for Can I approximate Schwartz functions which integrate to zero by $C_0^\infty$ functions which integrate to zero?
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| Jun 30, 2014 at 0:29 | comment | added | Christian Remling | @M Lemm: You're right, I was confused. In my "example", we would have to make $\varphi_n\sim 2^{-n}$ on $2^n<x<2^{n+1}$, and this part is $\sim 1/x$, so does not go to zero in $\mathcal S$. (The DC argument is fine, of course.) | |
| Jun 30, 2014 at 0:20 | comment | added | username | @Christian Remling:It's not clear to me that the approximation will work near the boundary of $B_{2^n}$ in the very strong Schwartz topology. What about using dominated convergence to prove that it is closed? Pointwise convergence is trivial and from uniform convergence of $(1+x^2)^{N/2+1}|f_n-f|$ one gets a dominating function. | |
| Jun 3, 2014 at 21:48 | history | edited | username | CC BY-SA 3.0 |
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| May 17, 2014 at 0:47 | vote | accept | username | ||
| May 17, 2014 at 0:34 | review | First posts | |||
| May 17, 2014 at 2:55 | |||||
| May 17, 2014 at 0:30 | answer | added | Christian Remling | timeline score: 6 | |
| May 17, 2014 at 0:16 | history | asked | username | CC BY-SA 3.0 |