KOEBE FUNCTION PDF
(c) Thinking of the Koebe function f as a map from the unit disk |z| < 1 to the complex plane, where does it fail to be one-to-one? Investigate this by looking at the. Looking for Koebe function? Find out information about Koebe function. The analytic function k = z -2= z + 2 z 2+ 3 z 3+ ⋯, that maps the unit disk onto the entire. Nonunivalent generalized Koebe function . of the Japan Academy, Series A, Mathematical Sciences, ; On harmonic combination of univalent functions.
|Published (Last):||2 April 2013|
|PDF File Size:||3.22 Mb|
|ePub File Size:||1.34 Mb|
|Price:||Free* [*Free Regsitration Required]|
Home Questions Tags Users Unanswered. The extremal case is given by the Koebe function or one of its rotations. I’m wondering if the following statement holds: Fhnction is how I ended up with this statement: Is this obviously wrong?
This is in response to a comment about rotating the Koebe function But this function cannot fix 1: Braindead 3, 17 Are you assuming that the derivative at the origin is equal to one? I’ll revise my question to make that clear. functon
Yamashita : Nonunivalent generalized Koebe function
It seems like a rather odd condition, unless you are assuming your functions to be real on the real axis. How does it arise?
I do ioebe understand your comment about the Koebe function in the edit. Your function should have az also in the numerator. However, of course this changes the derivative at the origin I thought I was using standard terminology, at least it’s the one used in Conway’s Complex Analysis Volume 2.
In that book, Koebe function and all of its “rotations” are functions of the form I wrote in my edit. In anycase, I have very specific normalization conditions, and just precomposing by rotation does not preserve them. The removed set is shown below in blue: In functkon, there is no extremal map. Sign up or log in Sign up using Google.