Regarding #2, what is a "former" function?
1. Prove that there is no analytic function insidesuch as every z in this region satysfies:Code:z:0<|z|<1.Code:f^2(z)=z
2. Let f be analytic at the annulus:.Code:D=z:0<|z-a|<r
Prove that if f has an antideriative function then Res(f,a)=0 .
Hope you'll be able to help me
Thanks a lot!
One way which I can think of is this : a function analytic inside a domain maps a closed contour to a closed contour. So assume there exists such a function. Now take a simple closed contour around the origin, and show that does not map it to a closed contour (use the argument principle, and the fact that inside the punctured disc).