Question

If $f(z)$ is a 1-to-1 analytic function on the unit disk and $f(0)=0$, show that there is an analytic function $g(z)$ such that $g(z)^2 = f(z^2)$.

score 447 · Answer 1 · 2022-07-12 22:30:06

If $f(z)$ is a 1-to-1 analytic function on the unit disk and $f(0)=0$, show that there is an analytic function $g(z)$ such that $g(z)^2 = f(z^2)$.

score 39 · Answer 2 · 2022-07-14 19:11:22

39

Views

"Mobius form" of a (meromorphic) function on $\mathbb{C}$

Published on 14 Jul 2022 - 19:11

score 167 · Answer 3 · 2022-07-14 20:52:24

167

Views

Suppose $f(z)$ is analytic on $\mathbb{C}\setminus\{0\}$ and $|f(z)| \leq |z|^{5/2} + |z|^{-1/2}$ for all $z\in \mathbb{C}\setminus\{0\}$...

Published on 14 Jul 2022 - 20:52

score 113 · Answer 4 · 2026-03-27 11:48:01

113

Views

Determine if analytic mappings from $\mathbb{C}\setminus \{0\}$ and $\mathbb{C}\setminus [0,\infty)$ to open unit disk exist and if so, find them...

Published on 27 Mar 2026 - 11:48

score 1.9k · Answer 5 · 2026-03-25 17:26:51

1.9k

Views

Suppose $f(z)$ is analytic on $|z|<1$ such that $|f(z)|<1$ for all $|z|<1$ and $f(0) = \alpha \neq 0$. Show $f(z) \neq 0$ for all $|z|<|\alpha|$.

Published on 25 Mar 2026 - 17:26

score 80 · Answer 6 · 2022-08-03 15:28:45

80

Views

$f(z)$ analytic on $D$ with sequence $z_n \in D$ s.t. $|f(z_n)| \to \infty$ as $n \to \infty$. Radius of convergence of power series for $f$ is 1?

Published on 03 Aug 2022 - 15:28

score 52 · Answer 7 · 2022-08-05 12:51:44

52

Views

Let $A$ be the set of points where the gradient of $u$ vanishes. If $A$ has an accumulation point in $\Omega$, is it true that $u$ is constant?

Published on 05 Aug 2022 - 12:51

score 148 · Answer 8 · 2022-08-07 06:49:10

148

Views

Zeros of an entire function $f(z)$

Published on 07 Aug 2022 - 6:49

score 98 · Answer 9 · 2022-08-14 14:41:11

98

Views

About square root of an analytic function

Published on 14 Aug 2022 - 14:41

score 84 · Answer 10 · 2026-03-29 02:29:09

84

Views

Is holomorph = analytic in several variables?

Published on 29 Mar 2026 - 2:29

score 157 · Answer 11 · 2022-08-19 18:08:33

157

Views

Domain/Definition of the Zeta Function

Published on 19 Aug 2022 - 18:08

score 51 · Answer 12 · 2022-08-25 10:30:38

51

Views

Clarification on proof of Laurent development (Conway)

Published on 25 Aug 2022 - 10:30

score 190 · Answer 13 · 2026-03-29 16:55:49

190

Views

Mobius transformations preserves uniform convergence

Published on 29 Mar 2026 - 16:55

score 217 · Answer 14 · 2022-09-03 08:14:07

217

Views

Are Lipschitz functions almost continuously differentiable in practice?

Published on 03 Sep 2022 - 8:14

score 207 · Answer 15 · 2022-09-04 14:09:44

207

Views

Understanding the proof of theorem 7.4 in Conway's book "Functions of one complex variable":

Published on 04 Sep 2022 - 14:09

List Question

If $f(z)$ is a 1-to-1 analytic function on the unit disk and $f(0)=0$, show that there is an analytic function $g(z)$ such that $g(z)^2 = f(z^2)$.

"Mobius form" of a (meromorphic) function on $\mathbb{C}$

Suppose $f(z)$ is analytic on $\mathbb{C}\setminus\{0\}$ and $|f(z)| \leq |z|^{5/2} + |z|^{-1/2}$ for all $z\in \mathbb{C}\setminus\{0\}$...

Determine if analytic mappings from $\mathbb{C}\setminus \{0\}$ and $\mathbb{C}\setminus [0,\infty)$ to open unit disk exist and if so, find them...

Suppose $f(z)$ is analytic on $|z|<1$ such that $|f(z)|<1$ for all $|z|<1$ and $f(0) = \alpha \neq 0$. Show $f(z) \neq 0$ for all $|z|<|\alpha|$.

$f(z)$ analytic on $D$ with sequence $z_n \in D$ s.t. $|f(z_n)| \to \infty$ as $n \to \infty$. Radius of convergence of power series for $f$ is 1?

Let $A$ be the set of points where the gradient of $u$ vanishes. If $A$ has an accumulation point in $\Omega$, is it true that $u$ is constant?

Zeros of an entire function $f(z)$

About square root of an analytic function

Is holomorph = analytic in several variables?

Domain/Definition of the Zeta Function

Clarification on proof of Laurent development (Conway)

Mobius transformations preserves uniform convergence

Are Lipschitz functions almost continuously differentiable in practice?

Understanding the proof of theorem 7.4 in Conway's book "Functions of one complex variable":

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