Timeline for Approximating linear bounded operator on $L^2([a,b])$
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Aug 11, 2021 at 22:07 | history | edited | YCor | CC BY-SA 4.0 |
formatting, removed signature (redundant)
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| Aug 11, 2021 at 17:50 | vote | accept | Peter Wacken | ||
| Aug 11, 2021 at 16:32 | answer | added | Christian Remling | timeline score: 2 | |
| Aug 11, 2021 at 16:07 | comment | added | Peter Wacken | @ChristianRemling I don't see how to derive a contradiction, because $g$ depends on $n$ here. Why can't $g$ be close to $\sin 2^n x$ while at the same time have a moderately growing $H^1_0$-norm? | |
| Aug 11, 2021 at 14:54 | comment | added | Christian Remling | I think for a counterexample you could consider something like $P(\sin nx)= \sin 2^n x$. Now an approximation of the desired type would have to map $\sin nx$ to functions $g$ with $\|g-\sin 2^n x\|_2<\epsilon$, $\|g'\|_2\le Cn$, which seems impossible (fix $\epsilon$, send $n\to\infty$). | |
| Aug 11, 2021 at 14:24 | history | asked | Peter Wacken | CC BY-SA 4.0 |