query: Show that there is an odd biholomorphic function $g$ on the unit disk such that $g(z)^2=f(z^2).$
positive_passages.docid: 148247
positive_passages.text: Prove the existence of an analytic function
negative_passages.docid: 136793
negative_passages.text: Does there exist a holomorphic function $\varphi(z)$ such that $\varphi^2(z) = \psi(z)$
negative_passages.docid: 63446
negative_passages.text: The existence of analytical branch of the logarithm of a holomorphic function
negative_passages.docid: 155245
negative_passages.text: root of an odd degree polynomial
negative_passages.docid: 149634
negative_passages.text: $ 2|f^{'}(0)| = \sup_{z, w \in D} |f(z)-f(w)|$
negative_passages.docid: 115824
negative_passages.text: Holomorphic functions which preserve orientation
negative_passages.docid: 6453
negative_passages.text: Let $n \geq 1$ be an odd integer. Show that $D_{2n}\cong \mathbb{Z}_2 \times D_n$.
negative_passages.docid: 74891
negative_passages.text: sum of holomorphic functions
negative_passages.docid: 46396
negative_passages.text: When can we find holomorphic bijections between annuli?
negative_passages.docid: 106971
negative_passages.text: Let $f:U \to V$ be a bijective holomorphic function. Show that inverse of $f$ is also holomorphic.
negative_passages.docid: 26687
negative_passages.text: Show that $f$ maps the unit circle to itself
negative_passages.docid: 144539
negative_passages.text: Power series $ f(g(z)) = z $
negative_passages.docid: 82458
negative_passages.text: Homeomorphism between the unit disc and the unit square
negative_passages.docid: 95632
negative_passages.text: Where is this function holomorphic?
negative_passages.docid: 74051
negative_passages.text: No analytic function in $\{|z|<1\}$ such that $f(0)=1$ and $|f(z)|\ge 1+|z|^2$. Proof strategy
negative_passages.docid: 65414
negative_passages.text: One-one analytic functions on unit disc
negative_passages.docid: 18877
negative_passages.text: $f(z)$ and $\overline{f(\overline{z})}$ simultaneously holomorphic