Question

Inequalities via Number of Zeros & Jensen's Formula

score 128 · Answer 1 · 2023-03-18 19:15:59

128

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Inequalities via Number of Zeros & Jensen's Formula

Published on 18 Mar 2023 - 19:15

score 197 · Answer 2 · 2023-04-04 02:29:07

197

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Many doubts about Stein & Shakarchi's Complex Analysis Question 5.2

Published on 04 Apr 2023 - 2:29

score 286 · Answer 3 · 2023-04-06 10:34:14

286

Views

Ratios of higher order derivatives with exponentially growing bound.

Published on 06 Apr 2023 - 10:34

score 154 · Answer 4 · 2023-04-11 05:46:28

154

Views

An example of a function $g:\mathbb R^2\to\mathbb R_{\geq 0}$ that is rotationally symmetric and "grows like $e^{\sigma t}$ in every direction".

Published on 11 Apr 2023 - 5:46

score 34 · Answer 5 · 2023-04-12 18:56:32

34

Views

Entire function taking real values on two parallel lines is periodic

Published on 12 Apr 2023 - 18:56

score 153 · Answer 6 · 2023-04-14 00:53:04

153

Views

Find all the entire functions satisfying $|f(z)|\leq-\ln(|z|^2)+|z|^2$, $f(0)=i$.

Published on 14 Apr 2023 - 0:53

score 50 · Answer 7 · 2023-05-12 06:57:17

50

Views

Extended Liouville to Real Part of Entire Functions

Published on 12 May 2023 - 6:57

score 64 · Answer 8 · 2023-05-25 00:57:45

64

Views

Question of the order of growth

Published on 25 May 2023 - 0:57

score 50 · Answer 9 · 2023-06-05 16:03:57

50

Views

All $f\in H(\mathbb{C})$ with $Re(f(z))=u(z)=u(x+iy)=x^2-y^2+2x+1$

Published on 05 Jun 2023 - 16:03

score 230 · Answer 10 · 2023-06-11 15:39:23

230

Views

Continuity of maximum modulus function $M(r)=\max_{|z|=r}|f(z)|$

Published on 11 Jun 2023 - 15:39

score 67 · Answer 11 · 2023-06-13 20:20:39

67

Views

Polya's representation (Boas Book)

Published on 13 Jun 2023 - 20:20

score 183 · Answer 12 · 2023-06-13 21:10:47

183

Views

An entire function $f(z)$ that is real if and only if $z$ is real

Published on 13 Jun 2023 - 21:10

score 51 · Answer 13 · 2023-06-24 17:02:00

51

Views

Want an example of entire function of order $\sqrt 2$

Published on 24 Jun 2023 - 17:02

score 114 · Answer 14 · 2023-06-29 19:28:57

114

Views

Prove that a function is a polynomial of degree at most one given $v(x,y) \geq x$

Published on 29 Jun 2023 - 19:28

score 83 · Answer 15 · 2023-07-07 21:52:25

83

Views

An entire function satisfying $f(z)=f(z+\xi t)$ for all $t\in\mathbb{R}$ and some $\xi\in\mathbb{C}$

Published on 07 Jul 2023 - 21:52

List Question

Inequalities via Number of Zeros & Jensen's Formula

Many doubts about Stein & Shakarchi's Complex Analysis Question 5.2

Ratios of higher order derivatives with exponentially growing bound.

An example of a function $g:\mathbb R^2\to\mathbb R_{\geq 0}$ that is rotationally symmetric and "grows like $e^{\sigma t}$ in every direction".

Entire function taking real values on two parallel lines is periodic

Find all the entire functions satisfying $|f(z)|\leq-\ln(|z|^2)+|z|^2$, $f(0)=i$.

Extended Liouville to Real Part of Entire Functions

Question of the order of growth

All $f\in H(\mathbb{C})$ with $Re(f(z))=u(z)=u(x+iy)=x^2-y^2+2x+1$

Continuity of maximum modulus function $M(r)=\max_{|z|=r}|f(z)|$

Polya's representation (Boas Book)

An entire function $f(z)$ that is real if and only if $z$ is real

Want an example of entire function of order $\sqrt 2$

Prove that a function is a polynomial of degree at most one given $v(x,y) \geq x$

An entire function satisfying $f(z)=f(z+\xi t)$ for all $t\in\mathbb{R}$ and some $\xi\in\mathbb{C}$

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