Timeline for Is there an example of a causally supported Schwartz function on $\mathbb{R}^4$ invariant under the Lorentz transform?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 30, 2023 at 1:54 | vote | accept | Isaac | ||
| Jan 29, 2023 at 22:22 | answer | added | Willie Wong | timeline score: 3 | |
| Jan 29, 2023 at 14:23 | comment | added | Isaac | Yes, that is right. I was mistaken about Lorentz invariance. | |
| Jan 29, 2023 at 4:35 | comment | added | Willie Wong | Ignoring the Lorentz invariance (which is impossible by what Andreas Blass said), are you looking for a Schwartz function that is non-zero EXACTLY on the set $0 < x_0^2 - x_1^2 - x_2^2 - x_3^3 < 4m^2$? | |
| Jan 28, 2023 at 23:24 | comment | added | Andreas Blass | I think I must not understand the question correctly in the Lorentz-invariant case. This invariance implies that $f$ is constant on the positive-time half of any hyperboloid $x^2=k$. Any such hyperboloid extends to arbitrarily large coordinate values, so $f$ can't tend to $0$ at large coordinate values unless it's identically $0$. | |
| Jan 28, 2023 at 19:52 | history | asked | Isaac | CC BY-SA 4.0 |