Question

If $f$ is a non-constant analytic function on $B$ such that $|f|$ is a constant on $\partial B$, then $f$ must have a zero in $B$

score 1.7k · Answer 1 · 2015-12-08 05:30:26

1.7k

Views

If $f$ is a non-constant analytic function on $B$ such that $|f|$ is a constant on $\partial B$, then $f$ must have a zero in $B$

Published on 08 Dec 2015 - 5:30

score 68 · Answer 2 · 2015-12-12 03:40:36

68

Views

Prove or disprove the following:$\{p_n\}$ converges uniformly to $f$ on $\{z\in \mathbb{C}: |z|=a\}$

Published on 12 Dec 2015 - 3:40

score 82 · Answer 3 · 2015-12-12 05:24:18

82

Views

Prove $v$ is harmonic and $\lim_{r \uparrow 1} v(re^{i\theta}) = 0$

Published on 12 Dec 2015 - 5:24

score 738 · Answer 4 · 2015-12-14 17:35:48

738

Views

An entire function such that $if(z)= \bar f(z)$ for all $z$ is constant

Published on 14 Dec 2015 - 17:35

score 675 · Answer 5 · 2015-12-14 18:16:22

675

Views

Showing $f(z)$ is constant when $Im(f^2(z)-f(z))=0$

Published on 14 Dec 2015 - 18:16

score 100 · Answer 6 · 2015-12-14 18:33:51

100

Views

Why does $v(z)=\text{Im}\left[\left(\frac{1+z}{1-z}\right)^2\right]$ not contradict maximum principle?

Published on 14 Dec 2015 - 18:33

score 657 · Answer 7 · 2015-12-21 03:25:27

657

Views

Some basic questions regarding the Maximum Principle for Harmonic Functions,

Published on 21 Dec 2015 - 3:25

score 1.3k · Answer 8 · 2015-12-25 10:00:51

1.3k

Views

Holomorphic function with a local maximum modulus is constant

Published on 25 Dec 2015 - 10:00

score 195 · Answer 9 · 2015-12-28 18:14:42

195

Views

Prove that $|f|\leq 1$ whenever $|x|\leq 1$.

Published on 28 Dec 2015 - 18:14

score 48 · Answer 10 · 2016-01-08 10:53:03

48

Views

Infinite number of points with modulus 1

Published on 08 Jan 2016 - 10:53

score 616 · Answer 11 · 2016-01-11 06:13:19

616

Views

Harmonic function zeros on open subset

Published on 11 Jan 2016 - 6:13

score 529 · Answer 12 · 2016-02-02 19:54:42

529

Views

How to classify harmonic functions on the punctured disk without the Schwartz reflection principle?

Published on 02 Feb 2016 - 19:54

score 620 · Answer 13 · 2016-02-13 19:07:05

620

Views

Maximum Principle of the Diffusion Equation

Published on 13 Feb 2016 - 19:07

score 1.3k · Answer 14 · 2016-02-14 05:22:41

1.3k

Views

Inhomogeneous Diffusion Equation - Maximum Principle

Published on 14 Feb 2016 - 5:22

score 328 · Answer 15 · 2016-02-16 17:04:02

328

Views

Maximum Principle for Nonlinear Heat Equation

Published on 16 Feb 2016 - 17:04

List Question

If $f$ is a non-constant analytic function on $B$ such that $|f|$ is a constant on $\partial B$, then $f$ must have a zero in $B$

Prove or disprove the following:$\{p_n\}$ converges uniformly to $f$ on $\{z\in \mathbb{C}: |z|=a\}$

Prove $v$ is harmonic and $\lim_{r \uparrow 1} v(re^{i\theta}) = 0$

An entire function such that $if(z)= \bar f(z)$ for all $z$ is constant

Showing $f(z)$ is constant when $Im(f^2(z)-f(z))=0$

Why does $v(z)=\text{Im}\left[\left(\frac{1+z}{1-z}\right)^2\right]$ not contradict maximum principle?

Some basic questions regarding the Maximum Principle for Harmonic Functions,

Holomorphic function with a local maximum modulus is constant

Prove that $|f|\leq 1$ whenever $|x|\leq 1$.

Infinite number of points with modulus 1

Harmonic function zeros on open subset

How to classify harmonic functions on the punctured disk without the Schwartz reflection principle?

Maximum Principle of the Diffusion Equation

Inhomogeneous Diffusion Equation - Maximum Principle

Maximum Principle for Nonlinear Heat Equation

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