Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.
|
|
|
|
Re: Riemann mapping theorem
Posted:
Mar 24, 2006 11:39 AM
|
|
"Lara" <the_brat_taz@yahoo.com> wrote in message
news:1143216397.311468.39610@i39g2000cwa.googlegroups.com...
> Show that for every conformal f: { z = x + iy , y >0} --->{ z = x + iy
> , y > 0}
> there exist a,b,c,d in R such that ad - bc = 1, f(z)= (az-b) / (cz-d)
>
> should we use Riemann mapping theorem ??
>
You shouldn't need anything as powerful as the Riemann mapping theorem.
Find two fractional linear transformations g and h such that go(foh) maps
the unit disc into the unit disc and such that g(f(h(0))) = 0.
________________________________
Eric J. Wingler (wingler@math.ysu.edu)
Dept. of Mathematics and Statistics
Youngstown State University
One University Plaza
Youngstown, OH 44555-0001
330-941-1817
|
|
|
|
