Timeline for Tauberian theorem $\sum_{k=1}^{\infty}e^{-\lambda_{k}t}c_{k} \xrightarrow{t\to 0} \sum_{k=1}^{\infty}c_{k} $
Current License: CC BY-SA 3.0
13 events
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| May 25, 2017 at 17:38 | comment | added | Christian Remling | @ThomasKojar: Well, I focused on the question you actually asked in the OP. I'm not sure I can do $\delta=o(k^{-1/2})$ in this style; already $O(k^{-1/2})$ might be tricky, though $O(k^{-1/2+\epsilon})$ is easy. But from Pietro's example, you can easily get $\delta_k=k^{-3/4}$, say, which has the desired asymptotics with $c_2=0$. | |
| May 25, 2017 at 15:09 | comment | added | Thomas Kojar | Because your $\lambda_{k}$ don't match the weyl asymptotics $\lambda_{k}\approx c_{1} k+c_{2}\sqrt{k}+O(\sqrt{k})$. | |
| May 25, 2017 at 14:58 | comment | added | Thomas Kojar | In your example, is it possible to keep the $\lambda_{k}$ fixed but change the $c_{k}$ accordingly? | |
| May 25, 2017 at 7:02 | comment | added | Pietro Majer | This may also suggest how to strengthen conveniently the assumptions in order to get the quantity (1) infinitesimal | |
| May 25, 2017 at 1:21 | history | edited | Christian Remling | CC BY-SA 3.0 |
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| May 25, 2017 at 1:09 | history | undeleted | Christian Remling | ||
| May 25, 2017 at 1:09 | history | edited | Christian Remling | CC BY-SA 3.0 |
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| May 24, 2017 at 18:55 | history | edited | Christian Remling | CC BY-SA 3.0 |
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| May 24, 2017 at 18:52 | history | deleted | Christian Remling | via Vote | |
| May 24, 2017 at 18:48 | history | edited | Christian Remling | CC BY-SA 3.0 |
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| May 24, 2017 at 18:41 | history | undeleted | Christian Remling | ||
| May 24, 2017 at 18:41 | history | deleted | Christian Remling | via Vote | |
| May 24, 2017 at 18:39 | history | answered | Christian Remling | CC BY-SA 3.0 |