Timeline for If $Z$ is standard normal and $f$ is analytic. Is $g(t)= E[ f(Z-t)]$ analytic?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Oct 9, 2017 at 15:12 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Sep 9, 2017 at 14:09 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Aug 10, 2017 at 14:01 | answer | added | user83457 | timeline score: 2 | |
| Aug 9, 2017 at 22:06 | comment | added | Christian Remling | @MateuszKwaśnicki: Yes, this is a good point, we will need control on $f$ on a strip or at least an open set containing $\mathbb R$. | |
| Aug 9, 2017 at 21:40 | comment | added | Mateusz Kwaśnicki | If $|f(x)| \leqslant |x|^4$ holds only on the real line, then I doubt the answer to the question is indeed "yes". At least, Morera's theorem cannot be applied directly: consider, for example, $f(x) = \exp(i \exp(x^2))$, which is bounded on the real line, but behaves badly in any strip $\{|\operatorname{Im} x| < \varepsilon\}$. | |
| Aug 9, 2017 at 20:44 | comment | added | Boby | @ChristianRemling But Morera is a tool from complex analysis, right? | |
| Aug 9, 2017 at 20:03 | history | asked | Boby | CC BY-SA 3.0 |