Timeline for Compactly supported smooth function with Laplace transform bounded on a cone
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 19, 2013 at 14:27 | comment | added | Shaoming | I don't see how $F$ being bounded implies $F$ being constant. For example $e^{-z^2}$ is bounded on the cone with forms an angle less than 45 degrees with the horizontal axis, but is not constant. | |
| Dec 19, 2013 at 6:59 | history | edited | Alexandre Eremenko | CC BY-SA 3.0 |
expanded the explanation
|
| Dec 18, 2013 at 22:39 | comment | added | Michael Renardy | The Fourier transform of $\phi$ is an entire function with exponential growth which is bounded on the real axis. If it is also bounded on another line through the origin, then the Phragmen-Lindelof Principle forces it to be constant. This allows only the trivial case $\phi=0$. | |
| Dec 18, 2013 at 19:52 | review | Low quality posts | |||
| Dec 18, 2013 at 20:56 | |||||
| Dec 18, 2013 at 19:46 | comment | added | Shaoming | Sorry I don't quite get it, could you say a bit more? How do we get the contradiction from the Phragmen–Lindelof principle? It just says the function is bounded, right? | |
| Dec 18, 2013 at 19:43 | comment | added | Gerald Edgar | In en.wikipedia.org/wiki/Phragmén–Lindelöf_principle, the Phragmén-Lindelöf Principle is about analytic functions. Maybe add an explanation showing how it applies here. | |
| Dec 18, 2013 at 19:33 | history | answered | Michael Renardy | CC BY-SA 3.0 |