Question

Show that a subset of $C(\mathbb{R})$ is compact with norm $\lVert u\rVert = \sup\lvert\frac{u(x)}{x^2 +1} \rvert$

score 66 · Answer 1 · 2020-06-29 17:21:20

66

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Show that a subset of $C(\mathbb{R})$ is compact with norm $\lVert u\rVert = \sup\lvert\frac{u(x)}{x^2 +1} \rvert$

Published on 29 Jun 2020 - 17:21

score 237 · Answer 2 · 2020-07-03 09:27:04

237

Views

Ascoli-Arzelà example and equicontinuity

Published on 03 Jul 2020 - 9:27

score 172 · Answer 3 · 2020-07-03 09:59:28

172

Views

Prove the relative compactness of a sequence in $L^p$

Published on 03 Jul 2020 - 9:59

score 54 · Answer 4 · 2020-07-26 01:02:35

54

Views

Why is the image under integration of a uniformly bounded subset of $C[a,b]$ necessarily compact?

Published on 26 Jul 2020 - 1:02

score 585 · Answer 5 · 2016-08-07 07:27:01

585

Views

Show that $\int_0^x f(t)dt$ is compact and injective

Published on 07 Aug 2016 - 7:27

score 656 · Answer 6 · 2016-09-03 15:31:28

656

Views

Showing a sequence of convex functions admits a uniformly convergent subsequence.

Published on 03 Sep 2016 - 15:31

score 189 · Answer 7 · 2016-09-25 17:50:30

189

Views

Consequences of the Arzelà–Ascoli theorem

Published on 25 Sep 2016 - 17:50

score 334 · Answer 8 · 2016-10-08 20:15:07

334

Views

A sequence in a family of continuous functions over a $\sigma$-compact metric space has a uniformly convergent subsequence

Published on 08 Oct 2016 - 20:15

score 193 · Answer 9 · 2016-11-05 23:31:09

193

Views

Prove that a subset G of $C([0,\pi])$ is relatively compact in $C([0,\pi])$

Published on 05 Nov 2016 - 23:31

score 809 · Answer 10 · 2016-12-03 20:03:17

809

Views

Arzela-Ascoli Counter Example?

Published on 03 Dec 2016 - 20:03

score 44 · Answer 11 · 2016-12-03 21:06:35

44

Views

What is definition of ε-tubes?

Published on 03 Dec 2016 - 21:06

score 91 · Answer 12 · 2017-01-24 21:08:26

91

Views

Proving that set of bounded stochastic processes is compact

Published on 24 Jan 2017 - 21:08

score 1k · Answer 13 · 2017-01-29 02:17:42

1k

Views

Applying Arzela-Ascoli to show pointwise convergence on $\mathbb{R}$.

Published on 29 Jan 2017 - 2:17

score 773 · Answer 14 · 2017-01-29 03:34:28

773

Views

Does this function sequence have a convergent subsequence?

Published on 29 Jan 2017 - 3:34

score 1.1k · Answer 15 · 2017-02-05 01:15:52

1.1k

Views

How to understand Arzela-Ascoli theorem?

Published on 05 Feb 2017 - 1:15

List Question

Show that a subset of $C(\mathbb{R})$ is compact with norm $\lVert u\rVert = \sup\lvert\frac{u(x)}{x^2 +1} \rvert$

Ascoli-Arzelà example and equicontinuity

Prove the relative compactness of a sequence in $L^p$

Why is the image under integration of a uniformly bounded subset of $C[a,b]$ necessarily compact?

Show that $\int_0^x f(t)dt$ is compact and injective

Showing a sequence of convex functions admits a uniformly convergent subsequence.

Consequences of the Arzelà–Ascoli theorem

A sequence in a family of continuous functions over a $\sigma$-compact metric space has a uniformly convergent subsequence

Prove that a subset G of $C([0,\pi])$ is relatively compact in $C([0,\pi])$

Arzela-Ascoli Counter Example?

What is definition of ε-tubes?

Proving that set of bounded stochastic processes is compact

Applying Arzela-Ascoli to show pointwise convergence on $\mathbb{R}$.

Does this function sequence have a convergent subsequence?

How to understand Arzela-Ascoli theorem?

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