L=sup{f''(0)|f in the set ...}


by niklas
Tags: lsupf0|f
niklas
niklas is offline
#1
Jun5-08, 06:23 PM
P: 4
Let [tex]D\subset\mathbb{C}[/tex] be the unitdisc and [tex]F=\{f:D\rightarrow D\,|\,\forall z\in D\partial_{\bar{z}}f=0\}[/tex], calculate [tex]L=\sup_{f\in F}|f''(0)|[/tex]. Show that there is an [tex]g\in F[/tex] with [tex]g''(0)=L[/tex].
I am a bit stuck. But I think that it might be an idea to start with Cauchy estimate. Any other ideas?
Phys.Org News Partner Science news on Phys.org
SensaBubble: It's a bubble, but not as we know it (w/ video)
The hemihelix: Scientists discover a new shape using rubber bands (w/ video)
Microbes provide insights into evolution of human language
niklas
niklas is offline
#2
Jun5-08, 07:31 PM
P: 4
[tex]
|a_n|\leq\frac{1}{2\pi}\frac{M}{r^3}l=\frac{M}{r^2}\quad M=\max_{|z|<r<1}|f(z)|=\sup_{z\in\partial D_r}|f(z)|
[/tex]
?
niklas
niklas is offline
#3
Jun5-08, 07:40 PM
P: 4
=1??


Register to reply