Timeline for Injectivity of two sided Laplace transform
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Mar 22, 2023 at 19:44 | vote | accept | Lau | ||
| Mar 22, 2023 at 13:28 | answer | added | Alexandre Eremenko | timeline score: 2 | |
| Mar 22, 2023 at 13:04 | comment | added | fedja | Yes. WLOG, $(a,b)=(-2\delta,2\delta)$. Then we have $e^{-\delta|x|}$ integrable with respect to $\mu$ and $\nu$, so we can write the LT of $\mu-\nu$ for complex arguments in the vertical strip around the imaginary axis and it will be analytic there. Being $0$ on $(-\delta,\delta)$, it has to be zero in the whole strip. But on the imaginary axis, it is just the Fourier transform, which determines a finite signed measure on $\mathbb R$ uniquely. | |
| Mar 22, 2023 at 11:59 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
minor typos
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| Mar 22, 2023 at 11:57 | history | asked | Lau | CC BY-SA 4.0 |