Question

limit of a holomorphic function

score 32 · Answer 1 · 2018-05-06 16:33:43

32

Views

limit of a holomorphic function

Published on 06 May 2018 - 16:33

score 429 · Answer 2 · 2026-03-25 07:46:27

429

Views

$P(z)$ be a monic polynomial with complex co-efficients of degree $n$ such that $|P(z)| \le 1, \forall |z| \le 1$ ; then is $P(z)=z^n$?

Published on 25 Mar 2026 - 7:46

score 534 · Answer 3 · 2018-05-07 17:00:30

534

Views

Show $f(z)=\int_{c} \frac{g(w)}{w-z}$ $dw$ is analytic on any domain $D$ not containing points of $C$

Published on 07 May 2018 - 17:00

score 185 · Answer 4 · 2026-03-25 06:04:51

185

Views

If $h$ is an arbitrary holomorphic function then there exist $\phi_1, \phi_2$ holomorphic such that $h = f\phi_1 + g\phi_2$

Published on 25 Mar 2026 - 6:04

score 577 · Answer 5 · 2018-05-08 14:26:59

577

Views

Checking whether a complex function has an antiderivative

Published on 08 May 2018 - 14:26

score 60 · Answer 6 · 2018-05-09 10:29:42

60

Views

Complex Analysis : A function satisfying certain conditions , a counterexample?

Published on 09 May 2018 - 10:29

score 400 · Answer 7 · 2026-03-25 09:22:52

400

Views

Composition of a subharmonic function and a holomorphic function is harmonic.

Published on 25 Mar 2026 - 9:22

score 63 · Answer 8 · 2018-05-10 10:22:33

63

Views

Function defined by Cauchy Integral

Published on 10 May 2018 - 10:22

score 63 · Answer 9 · 2026-03-25 09:05:55

63

Views

Is there an analytically continued function of $z^p$ at zero?

Published on 25 Mar 2026 - 9:05

score 211 · Answer 10 · 2018-05-10 18:09:51

211

Views

existence of holomorphic function in the unit disc such that $f\Big(\frac{1}{2n}\Big)=f\Big(\frac{1}{2n+1}\Big)$

Published on 10 May 2018 - 18:09

score 302 · Answer 11 · 2026-03-25 06:07:04

302

Views

Holomorphic function $f: \Bbb C \rightarrow \Bbb C$ such that $|f(z)|\leq C|\negthinspace\cos(z)|$ for all $z \in \Bbb C$

Published on 25 Mar 2026 - 6:07

score 182 · Answer 12 · 2026-03-22 01:22:45

182

Views

Normal family of complex functions

Published on 22 Mar 2026 - 1:22

score 725 · Answer 13 · 2018-05-13 00:17:40

725

Views

Injective holomorphic functions on $\mathbb{C} \setminus \{0\}$

Published on 13 May 2018 - 0:17

score 65 · Answer 14 · 2018-05-13 03:58:13

65

Views

Regarding $A(D)$ and $H^\infty(D)$

Published on 13 May 2018 - 3:58

score 125 · Answer 15 · 2026-03-25 04:19:10

125

Views

Let $f:B_1(0) \rightarrow B_1(0)$ be a holomorphic function with at least two fixed pionts. Show $f=id$.

Published on 25 Mar 2026 - 4:19

List Question

limit of a holomorphic function

$P(z)$ be a monic polynomial with complex co-efficients of degree $n$ such that $|P(z)| \le 1, \forall |z| \le 1$ ; then is $P(z)=z^n$?

Show $f(z)=\int_{c} \frac{g(w)}{w-z}$ $dw$ is analytic on any domain $D$ not containing points of $C$

If $h$ is an arbitrary holomorphic function then there exist $\phi_1, \phi_2$ holomorphic such that $h = f\phi_1 + g\phi_2$

Checking whether a complex function has an antiderivative

Complex Analysis : A function satisfying certain conditions , a counterexample?

Composition of a subharmonic function and a holomorphic function is harmonic.

Function defined by Cauchy Integral

Is there an analytically continued function of $z^p$ at zero?

existence of holomorphic function in the unit disc such that $f\Big(\frac{1}{2n}\Big)=f\Big(\frac{1}{2n+1}\Big)$

Holomorphic function $f: \Bbb C \rightarrow \Bbb C$ such that $|f(z)|\leq C|\negthinspace\cos(z)|$ for all $z \in \Bbb C$

Normal family of complex functions

Injective holomorphic functions on $\mathbb{C} \setminus \{0\}$

Regarding $A(D)$ and $H^\infty(D)$

Let $f:B_1(0) \rightarrow B_1(0)$ be a holomorphic function with at least two fixed pionts. Show $f=id$.

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