Timeline for Fourier transform property in Feynman 1986 Dirac Memorial Lecture
Current License: CC BY-SA 4.0
5 events
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| Mar 6, 2019 at 9:34 | comment | added | Luca | I just came across this book [Fourier Analysis, Self-Adjointness. Michael Reed, Barry Simon ](elsevier.com/books/ii-fourier-analysis-self-adjointness/reed/…) offering a free preview of page 19, which is indeed introducing the subject basically on the same lines as you sketched. Though running through the details of the various demonstrations appears quite demanding. | |
| Mar 5, 2019 at 14:55 | comment | added | mike stone | @Luca Agreed. It's a sketch of what Feynman must have had in mind. What one needs is sufficient conditions to make the boundary value $f(t)$ analytic. Sufficiently fast vanishing of $F(\omega)$ as $\omega$ gets large should be enough. I'm pretty sure that if $|F(\omega)|$ is bounded by an exponential $e^{-\mu \omega}$, $\mu>0$ then $f(t)$ will be analytic on the real axis and then the claimed result holds. | |
| Mar 5, 2019 at 14:49 | comment | added | Luca | I am not sure whether that is a proof or just a sketch of how yourself would proceed to prove such a theorem. In that case, I am afraid I am not proficient enough to complete that sketch on my own. But sure, somewhere there shall exist a rigorous proof precisely identifying said "certain properties". | |
| Mar 5, 2019 at 13:23 | history | edited | mike stone | CC BY-SA 4.0 |
added 62 characters in body
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| Mar 5, 2019 at 13:14 | history | answered | mike stone | CC BY-SA 4.0 |