Timeline for Does $\sum_{n=1}^\infty e^{-n^2 T} \int_0^T e^{n^2 t} \lvert f(t)\rvert \, dt$ converge for $L^1_\text{loc}$ $f : [0,\infty) \to \mathbb{R}$?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Jul 21, 2023 at 16:42 | comment | added | Isaac | Oh yes. You are absolutely right. | |
| Jul 21, 2023 at 16:40 | comment | added | Aleksei Kulikov | @Isaac Almost, to be precise, in $L^1_{loc}(0, \infty)$, I didn't look at what happens near $0$. | |
| Jul 21, 2023 at 15:55 | comment | added | Isaac | So, it seems that my series is also in $L^1_{loc}[0,\infty)$ according to your argument? | |
| Jul 21, 2023 at 15:34 | comment | added | Isaac | Yes, $n^2$ indeed seems crucial. Thank you for your answer. | |
| Jul 21, 2023 at 15:32 | vote | accept | Isaac | ||
| Jul 21, 2023 at 14:51 | history | edited | Aleksei Kulikov | CC BY-SA 4.0 |
deleted 3 characters in body
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| Jul 21, 2023 at 14:31 | history | answered | Aleksei Kulikov | CC BY-SA 4.0 |