Timeline for Can curves induced by analytic maps wiggle infinitely across a line?
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 22, 2010 at 22:53 | vote | accept | Henry Yuen | ||
| Apr 22, 2010 at 17:39 | comment | added | Robin Chapman | Each $f(t_j)/t_j^n$ is real. As $j\to\infty$, $t_j\to0$ and so $f(t_j)/t_j^n\to a_n$. As the limit of a sequence of real numbers, $a_n$ is real. | |
| Apr 22, 2010 at 17:18 | comment | added | Henry Yuen | I follow everything, except for the base step to establish $a_n\in\mathbb{R}$. I presume that it's because $f(z)/z^n$ has an accumulation of real values on values from the $[0,1]$ interval, and since the image of $[0,1]$ contains the accumulation point, $f(0)/0^n = a_n$ must be real valued as well. | |
| Apr 22, 2010 at 12:12 | comment | added | gowers | Very nice. My mistake was to try to use the no-isolated-zeros theorem rather than imitating its proof. | |
| Apr 22, 2010 at 7:26 | history | answered | Robin Chapman | CC BY-SA 2.5 |