Question

Locally bounded $\Leftrightarrow$ compactness

score 957 · Answer 1 · 2026-02-23 07:57:39

957

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Locally bounded $\Leftrightarrow$ compactness

Published on 23 Feb 2026 - 7:57

score 202 · Answer 2 · 2026-04-05 17:08:19

202

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Q. Normal operator and properties

Published on 05 Apr 2026 - 17:08

score 573 · Answer 3 · 2026-02-23 08:07:08

573

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Prove that if $\mathcal{F}'$ is normal and $\sup_{f ∈ \mathcal{F}} \{ |f(z_0)| \} < +∞$, then $\mathcal{F}$ is normal

Published on 23 Feb 2026 - 8:07

score 797 · Answer 4 · 2026-02-23 08:05:00

797

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Is there a flaw in this proof of Marty's theorem (normal families)?

Published on 23 Feb 2026 - 8:05

score 6.7k · Answer 5 · 2026-02-23 08:03:48

6.7k

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The family of analytic functions with positive real part is normal

Published on 23 Feb 2026 - 8:03

score 1.3k · Answer 6 · 2026-02-23 08:07:02

1.3k

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The family $\{ f(kz)\}_{k \in \mathbb C}$ with $f$ entire is normal in the annulus $r_1<|z|<r_2$ iff $f$ is a polynomial

Published on 23 Feb 2026 - 8:07

score 526 · Answer 7 · 2026-02-23 08:07:08

526

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Additional hypotheses needed for the converse of $\mathscr F \subset H(G)$ normal $\implies$ $\mathscr F ' = \{f' : f \in \mathscr F\}$ normal?

Published on 23 Feb 2026 - 8:07

score 336 · Answer 8 · 2026-02-23 08:03:14

336

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Proof of the three-point characterization of holomorphy

Published on 23 Feb 2026 - 8:03

score 335 · Answer 9 · 2026-02-23 08:07:02

335

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$\{f_n\}$ be a normal family on $V$ s.t. $\{z \in V : \lim _{n\to \infty} f_n(z)$ exists $\}$ has a limit point in $V$

Published on 23 Feb 2026 - 8:07

score 189 · Answer 10 · 2026-02-23 08:03:48

189

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An equivalent condition to show a family of holomorphic functions is normal

Published on 23 Feb 2026 - 8:03

score 383 · Answer 11 · 2026-04-05 23:38:41

383

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A problem of normal families

Published on 05 Apr 2026 - 23:38

score 2.7k · Answer 12 · 2026-02-23 08:03:36

2.7k

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Prove that the family of functions is normal

Published on 23 Feb 2026 - 8:03

score 749 · Answer 13 · 2026-02-23 08:03:15

749

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Show a certain subset of $\mathcal{O}(\mathbb{H})$ is a normal family

Published on 23 Feb 2026 - 8:03

score 1.3k · Answer 14 · 2026-04-05 18:38:36

1.3k

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A question about normal families

Published on 05 Apr 2026 - 18:38

score 136 · Answer 15 · 2026-02-23 08:05:04

136

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Family of functions with $f(0) = 0$ and $f(\mathbb{D}) \cap [1,2] = \emptyset$ is normal

Published on 23 Feb 2026 - 8:05

List Question

Locally bounded $\Leftrightarrow$ compactness

Q. Normal operator and properties

Prove that if $\mathcal{F}'$ is normal and $\sup_{f ∈ \mathcal{F}} \{ |f(z_0)| \} < +∞$, then $\mathcal{F}$ is normal

Is there a flaw in this proof of Marty's theorem (normal families)?

The family of analytic functions with positive real part is normal

The family $\{ f(kz)\}_{k \in \mathbb C}$ with $f$ entire is normal in the annulus $r_1<|z|<r_2$ iff $f$ is a polynomial

Additional hypotheses needed for the converse of $\mathscr F \subset H(G)$ normal $\implies$ $\mathscr F ' = \{f' : f \in \mathscr F\}$ normal?

Proof of the three-point characterization of holomorphy

$\{f_n\}$ be a normal family on $V$ s.t. $\{z \in V : \lim _{n\to \infty} f_n(z)$ exists $\}$ has a limit point in $V$

An equivalent condition to show a family of holomorphic functions is normal

A problem of normal families

Prove that the family of functions is normal

Show a certain subset of $\mathcal{O}(\mathbb{H})$ is a normal family

A question about normal families

Family of functions with $f(0) = 0$ and $f(\mathbb{D}) \cap [1,2] = \emptyset$ is normal

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