Question

Show that a class of holomorphic functions is a normal family.

score 1.3k · Answer 1 · 2015-01-04 15:49:02

1.3k

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Show that a class of holomorphic functions is a normal family.

Published on 04 Jan 2015 - 15:49

score 588 · Answer 2 · 2015-03-18 11:28:14

588

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The Set of Functions satisfying $\int_{D}\vert f(z)\vert (1-\vert z\vert)^2dA(z)\le 1$ is a Normal Family

Published on 18 Mar 2015 - 11:28

score 7.7k · Answer 3 · 2015-05-11 16:55:25

7.7k

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Scaling Normal Distribution

Published on 11 May 2015 - 16:55

score 2k · Answer 4 · 2015-05-17 14:56:33

2k

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Explicit example of normal family

Published on 17 May 2015 - 14:56

score 687 · Answer 5 · 2015-05-30 18:16:33

687

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Family of analytic functions from unit disk to the plane minus a line

Published on 30 May 2015 - 18:16

score 174 · Answer 6 · 2015-07-11 04:09:11

Let $\{f_n\}_{n=1}^{\infty}$ be such that $f_1(z)=\sin(z)$, and $f_{n+1}(z)=\sin(f_n(z))$. Show $\{f_n\}$ is not locally bounded near the origin.

score 235 · Answer 7 · 2015-08-05 23:34:42

235

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Let $f$ be such that $f(0)=0$ and $f'(0)=1$. Find iff conditions for normality of successive iterations $f\circ f\circ\ldots$

Published on 05 Aug 2015 - 23:34

score 250 · Answer 8 · 2015-08-17 02:24:33

250

Views

Partial converse to $\mathcal{F}$ normal implies $\mathcal{F}$' normal.

Published on 17 Aug 2015 - 2:24

score 171 · Answer 9 · 2015-08-22 12:20:21

171

Views

Dettman's Applied Complex Variables Theorem 4.2.5 Correction (Normal Families)

Published on 22 Aug 2015 - 12:20

score 107 · Answer 10 · 2015-09-22 01:44:02

107

Views

distance of the 'waist' of a caustic in a parabola

Published on 22 Sep 2015 - 1:44

score 2.6k · Answer 11 · 2015-12-09 14:44:35

2.6k

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When does the normality of the family of derivatives imply that the family itself is normal?

Published on 09 Dec 2015 - 14:44

score 116 · Answer 12 · 2015-12-18 05:58:11

116

Views

Maximizing Area from Family of Biholomorphic Functions of Unit Disk

Published on 18 Dec 2015 - 5:58

score 100 · Answer 13 · 2016-01-12 07:12:03

100

Views

Full Strength of Arzela-Ascoli

Published on 12 Jan 2016 - 7:12

score 115 · Answer 14 · 2016-01-14 08:10:05

115

Views

Contour Integral Inequality and Normal Families

Published on 14 Jan 2016 - 8:10

score 690 · Answer 15 · 2016-01-14 16:07:32

690

Views

Show that a family of univalent functions, $f_n(0)=0$, $f_n'(0)=1$ is a normal family.

Published on 14 Jan 2016 - 16:07

List Question

Show that a class of holomorphic functions is a normal family.

The Set of Functions satisfying $\int_{D}\vert f(z)\vert (1-\vert z\vert)^2dA(z)\le 1$ is a Normal Family

Scaling Normal Distribution

Explicit example of normal family

Family of analytic functions from unit disk to the plane minus a line

Let $\{f_n\}_{n=1}^{\infty}$ be such that $f_1(z)=\sin(z)$, and $f_{n+1}(z)=\sin(f_n(z))$. Show $\{f_n\}$ is not locally bounded near the origin.

Let $f$ be such that $f(0)=0$ and $f'(0)=1$. Find iff conditions for normality of successive iterations $f\circ f\circ\ldots$

Partial converse to $\mathcal{F}$ normal implies $\mathcal{F}$' normal.

Dettman's Applied Complex Variables Theorem 4.2.5 Correction (Normal Families)

distance of the 'waist' of a caustic in a parabola

When does the normality of the family of derivatives imply that the family itself is normal?

Maximizing Area from Family of Biholomorphic Functions of Unit Disk

Full Strength of Arzela-Ascoli

Contour Integral Inequality and Normal Families

Show that a family of univalent functions, $f_n(0)=0$, $f_n'(0)=1$ is a normal family.

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