Question

If $|f|+|g|$ is constant on $D,$ prove that holomorphic functions $f,~g$ are constant on $D$.

score 1.4k · Answer 1 · 2017-01-03 23:20:31

1.4k

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If $|f|+|g|$ is constant on $D,$ prove that holomorphic functions $f,~g$ are constant on $D$.

Published on 03 Jan 2017 - 23:20

score 99 · Answer 2 · 2017-01-04 12:06:02

99

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Theorem about inverse of holomorphic $f = u + iv$

Published on 04 Jan 2017 - 12:06

score 56 · Answer 3 · 2017-01-05 15:48:57

56

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understanding holomorphic Functions

Published on 05 Jan 2017 - 15:48

score 59 · Answer 4 · 2017-01-05 15:53:04

59

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Find an analytic function $w=u+iv$ such that $u=\frac{x(1-x^2-y^2)}{4x^2y^2+(1+y^2-x^2)^2}, w(0)=0$

Published on 05 Jan 2017 - 15:53

score 193 · Answer 5 · 2026-03-25 13:56:24

193

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On upper bounds of the complex modulus of the Mellin transform of the cosine function, when is restricted to a given rectangle

Published on 25 Mar 2026 - 13:56

score 133 · Answer 6 · 2017-01-06 11:39:44

133

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Example of holomorphic function satisfying certain properties

Published on 06 Jan 2017 - 11:39

score 72 · Answer 7 · 2017-01-09 14:29:27

72

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Proof that two conditions imply that a function $f$ is constant

Published on 09 Jan 2017 - 14:29

score 912 · Answer 8 · 2017-01-10 21:42:21

912

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Schwarz's Lemma exercise

Published on 10 Jan 2017 - 21:42

score 239 · Answer 9 · 2017-01-11 08:13:12

239

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If $f(z)^N$ is analytic then $f(z)$ is analytic

Published on 11 Jan 2017 - 8:13

score 1.3k · Answer 10 · 2017-01-13 23:50:53

1.3k

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$f,g \in H(\mathbb{C})$ s.t. $|f(z)| \le k|g(z)|$ $\implies$ $f(z) = cg(z)$

Published on 13 Jan 2017 - 23:50

score 73 · Answer 11 · 2017-01-14 00:32:51

73

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Holomorphic functions in the disc $D(0,r)$ that satisfy certain properties

Published on 14 Jan 2017 - 0:32

score 91 · Answer 12 · 2017-01-14 22:03:14

91

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Existence of zeroes of holomorphic Functions

Published on 14 Jan 2017 - 22:03

score 248 · Answer 13 · 2017-01-14 22:32:50

248

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No holomorphic logarithmn

Published on 14 Jan 2017 - 22:32

score 1.5k · Answer 14 · 2017-01-14 22:34:40

1.5k

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Proof that conformal maps (statisfying certain conditions) are holomorphic/antiholomorphic

Published on 14 Jan 2017 - 22:34

score 135 · Answer 15 · 2017-01-17 11:36:16

135

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Prove that there is no $v$ such that $f = \ln(x^2+y^2) + iv$ is holomorphic

Published on 17 Jan 2017 - 11:36

List Question

If $|f|+|g|$ is constant on $D,$ prove that holomorphic functions $f,~g$ are constant on $D$.

Theorem about inverse of holomorphic $f = u + iv$

understanding holomorphic Functions

Find an analytic function $w=u+iv$ such that $u=\frac{x(1-x^2-y^2)}{4x^2y^2+(1+y^2-x^2)^2}, w(0)=0$

On upper bounds of the complex modulus of the Mellin transform of the cosine function, when is restricted to a given rectangle

Example of holomorphic function satisfying certain properties

Proof that two conditions imply that a function $f$ is constant

Schwarz's Lemma exercise

If $f(z)^N$ is analytic then $f(z)$ is analytic

$f,g \in H(\mathbb{C})$ s.t. $|f(z)| \le k|g(z)|$ $\implies$ $f(z) = cg(z)$

Holomorphic functions in the disc $D(0,r)$ that satisfy certain properties

Existence of zeroes of holomorphic Functions

No holomorphic logarithmn

Proof that conformal maps (statisfying certain conditions) are holomorphic/antiholomorphic

Prove that there is no $v$ such that $f = \ln(x^2+y^2) + iv$ is holomorphic

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