Timeline for Convergence to a $C^\infty$ function
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Mar 17, 2019 at 15:48 | comment | added | James Baxter | Ah, you’re right. | |
| Mar 17, 2019 at 15:45 | history | edited | James Baxter | CC BY-SA 4.0 |
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| Mar 17, 2019 at 15:08 | comment | added | Dap | Unless I've misunderstood, this has easy counterexamples. Take a sequence of smooth functions $f_n$ converging uniformly to a non-smooth function. Set $g(n,\epsilon)=\epsilon^{-n}f_n$ if $\lceil 1/(1-\epsilon)\rceil=n,$ and set $g(n,\epsilon)=0$ otherwise. This gives $\sum_{n=1}^\infty g(n,\epsilon)=f_{\lceil 1/(1-\epsilon)\rceil}.$ | |
| Mar 17, 2019 at 14:55 | comment | added | Wojowu | In the middle paragraph, shouldn't it be $\lim_{N\to\infty}$? Also, in the last paragraph, shouldn't the sum be up to infinity? | |
| Mar 17, 2019 at 14:20 | history | edited | James Baxter | CC BY-SA 4.0 |
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| Mar 17, 2019 at 13:18 | history | edited | James Baxter | CC BY-SA 4.0 |
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| Mar 17, 2019 at 13:13 | history | asked | James Baxter | CC BY-SA 4.0 |