Question

Relaxing the identity theorem

score 92 · Answer 1 · 2017-07-29 08:27:22

92

Views

Relaxing the identity theorem

Published on 29 Jul 2017 - 8:27

score 346 · Answer 2 · 2017-08-03 21:58:33

346

Views

Prove that a holomorphic function has a finite limit as $\Im(z)\to\infty$.

Published on 03 Aug 2017 - 21:58

score 109 · Answer 3 · 2017-08-10 19:00:35

109

Views

Is a holomorhpic function with these properties the constant $0$?

Published on 10 Aug 2017 - 19:00

score 113 · Answer 4 · 2017-08-14 11:24:37

113

Views

Why is $\oint_p \frac{1}{z} dz=0$ in simply connected regions?

Published on 14 Aug 2017 - 11:24

score 101 · Answer 5 · 2017-08-22 10:43:12

101

Views

Name of theorem for holomorphic function

Published on 22 Aug 2017 - 10:43

score 1.2k · Answer 6 · 2017-08-22 19:41:19

1.2k

Views

Biholomorphic functions on unit disc

Published on 22 Aug 2017 - 19:41

score 855 · Answer 7 · 2017-08-24 14:40:43

$f$ is continuous in $\mathbb{C}$ and holomorphic in $U=\{z\in\mathbb{C}:\operatorname{Im} z\neq 0\}$, then $f$ is holomorphic in $\mathbb{C}$

score 83 · Answer 8 · 2017-08-28 01:33:46

83

Views

Unif convergence of sequences of infinitely diff complex functions does not imply uniform convergence of derivative on compact sets.

Published on 28 Aug 2017 - 1:33

score 743 · Answer 9 · 2017-09-01 20:50:54

743

Views

Why do you require connection in the open mapping theorem and maximum modulus principle?

Published on 01 Sep 2017 - 20:50

score 790 · Answer 10 · 2017-09-05 17:13:24

790

Views

Show that holomorphic function $f$ is constant if $\Re f$ or $\Im f$ or $|f|$ is constant without using Cauchy Riemann equations

Published on 05 Sep 2017 - 17:13

score 112 · Answer 11 · 2017-09-05 21:34:33

112

Views

Either $f$ is a polynomial or $|f(z_j)| > e^{n|z_j|}. $

Published on 05 Sep 2017 - 21:34

score 1.2k · Answer 12 · 2017-09-06 08:31:21

1.2k

Views

A function is analytic if and only if it is holomorphic

Published on 06 Sep 2017 - 8:31

score 738 · Answer 13 · 2017-09-08 18:04:23

738

Views

Let $f(x+iy) = u(x,y) + iv(x,y)$ be a holomorphic function on $\Omega \subset \mathbb{C}$, where $u\cdot v = 1$. Prove that $f$ must be constant.

Published on 08 Sep 2017 - 18:04

score 2k · Answer 14 · 2017-09-09 12:22:00

2k

Views

$f(z)$ is holomorphic, prove that $g(z) = \overline{f(\overline{z})}$ is holomorphic.

Published on 09 Sep 2017 - 12:22

score 55 · Answer 15 · 2017-09-12 14:53:45

55

Views

Justify $ f(z)g(z) := \sum\limits_{j=0}^{\infty}\varphi_j z^j$ for $|z|\leq 1$

Published on 12 Sep 2017 - 14:53

List Question

Relaxing the identity theorem

Prove that a holomorphic function has a finite limit as $\Im(z)\to\infty$.

Is a holomorhpic function with these properties the constant $0$?

Why is $\oint_p \frac{1}{z} dz=0$ in simply connected regions?

Name of theorem for holomorphic function

Biholomorphic functions on unit disc

$f$ is continuous in $\mathbb{C}$ and holomorphic in $U=\{z\in\mathbb{C}:\operatorname{Im} z\neq 0\}$, then $f$ is holomorphic in $\mathbb{C}$

Unif convergence of sequences of infinitely diff complex functions does not imply uniform convergence of derivative on compact sets.

Why do you require connection in the open mapping theorem and maximum modulus principle?

Show that holomorphic function $f$ is constant if $\Re f$ or $\Im f$ or $|f|$ is constant without using Cauchy Riemann equations

Either $f$ is a polynomial or $|f(z_j)| > e^{n|z_j|}. $

A function is analytic if and only if it is holomorphic

Let $f(x+iy) = u(x,y) + iv(x,y)$ be a holomorphic function on $\Omega \subset \mathbb{C}$, where $u\cdot v = 1$. Prove that $f$ must be constant.

$f(z)$ is holomorphic, prove that $g(z) = \overline{f(\overline{z})}$ is holomorphic.

Justify $ f(z)g(z) := \sum\limits_{j=0}^{\infty}\varphi_j z^j$ for $|z|\leq 1$

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