Timeline for Extending a function from $\mathbb{Q}$ to the upper half plane $\mathbb{H}\cup\mathbb{Q}\cup\{i\infty\}$
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 8, 2014 at 2:04 | comment | added | Alexandre Eremenko | Igor, I do not see how transplanting to the disc makes the problem easier. Poisson extension is good for continuous function on the unit circle. | |
| Feb 7, 2014 at 23:18 | comment | added | Igor Rivin | @MattYoung Yes, that's what I think, too. | |
| Feb 7, 2014 at 22:06 | comment | added | Matt Young | I think the interesting examples will not be continuous when restricted to the real line. The question as stated may be too broad. | |
| Feb 7, 2014 at 21:42 | comment | added | Igor Rivin | @MattYoung Really? Who knew! But seriously: first extend your function in your favorite way to the real axis, and then Poisson-extend. If you want your function to be continuous, then there is (at most) one way to extend to the real line. If not, there is nothing canonical, as far as I can tell. | |
| Feb 7, 2014 at 21:00 | comment | added | Matt Young | I don't quite see the connection here. The extended function may not have any nice properties when restricted to the real line. The rationals are measure zero. | |
| Feb 7, 2014 at 18:57 | history | answered | Igor Rivin | CC BY-SA 3.0 |