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

  • Thread starter niklas
  • Start date
  • #1
4
0

Main Question or Discussion Point

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?
 
Last edited:

Answers and Replies

  • #2
4
0
[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]
?
 
Last edited:
  • #3
4
0
=1??
 

Related Threads for: L=sup{f''(0)|f in the set }

Replies
11
Views
3K
  • Last Post
Replies
17
Views
4K
Replies
5
Views
2K
  • Last Post
Replies
4
Views
6K
Replies
5
Views
881
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
5
Views
2K
Replies
10
Views
2K
Top