Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Say I have a lacunary $q$ series $s(q)=\sum_{n=0}^{\infty} a_{n}q^{n}$ , and I have a quasiconformal transformation $\xi$ which preserves the boundary of the unit disk in $\mathbb{C}$ such that if $|q|=1$ then $|\xi(q)|=1$. Is there a method from Teichmüller theory that allows us to explicitly write down the coefficients $b_{n}$ of $s(\xi(q)) = \sum_{n=0}^{\infty} a_{n}\xi(q)^{n} = \sum_{n=0}^{\infty} b_{n}q^{n}$ given some explicit $\xi$?

share|improve this question

1 Answer 1

The answer is no: pick $s(q)=q$ to be simply the identity, then you would obtain automatically a power series expansion for any quasiconformal $\xi$ preserving the circle, which can't be true since there are some $\xi$ that are not analytic near the origin...

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.