Question

Show that $f_n(x) = x^n$ defines a sequence of equicontinuous functions...

score 569 · Answer 1 · 2021-08-10 01:27:53

569

Views

Show that $f_n(x) = x^n$ defines a sequence of equicontinuous functions...

Published on 10 Aug 2021 - 1:27

score 296 · Answer 2 · 2021-08-13 09:16:20

296

Views

Rudin's PMA Theorem 7.25

Published on 13 Aug 2021 - 9:16

score 174 · Answer 3 · 2021-08-31 13:24:15

174

Views

Show that F is not equicontinuous

Published on 31 Aug 2021 - 13:24

score 64 · Answer 4 · 2021-09-11 19:36:15

64

Views

Equivalent condition for equicontinuity of a sequence

Published on 11 Sep 2021 - 19:36

score 71 · Answer 5 · 2026-02-23 21:39:46

71

Views

Pointwise convergence of $F_n(t) = \max_{y \in \mathbb R^N} \int_{B_t(y)} |u_n|^2 \ dx$

Published on 23 Feb 2026 - 21:39

score 163 · Answer 6 · 2026-02-23 21:39:01

163

Views

How can we derive the Arzelà-Ascoli theorem for a $\sigma$-compact space from the ordinary Arzelà-Ascoli theorem?

Published on 23 Feb 2026 - 21:39

score 31 · Answer 7 · 2026-02-23 21:39:46

31

Views

If $(\varphi_n)$ is uniformly equicontinuous and $0\le f_n\le-3\ln\varphi_n$, show that $(f_n)$ is equicontinuous at $0$

Published on 23 Feb 2026 - 21:39

score 73 · Answer 8 · 2026-02-23 21:37:37

73

Views

Continuous extension in the proof of Arzela - Ascoli theorem

Published on 23 Feb 2026 - 21:37

score 162 · Answer 9 · 2021-11-23 09:53:39

162

Views

$L^2$ Compactness with the Fourier Transform, Fréchet-Kolmogorov-Riesz theorem

Published on 23 Nov 2021 - 9:53

score 342 · Answer 10 · 2021-12-02 23:00:20

342

Views

Equicontinuity + pointwise convergence implies uniform continuity

Published on 02 Dec 2021 - 23:00

score 85 · Answer 11 · 2026-02-23 21:35:46

85

Views

Given a bounded sequence in $L^1([a,b])$, is $(t\mapsto \int_a^t f_n \,\mathrm d\lambda)_n$ equicontinuous?

Published on 23 Feb 2026 - 21:35

score 282 · Answer 12 · 2021-12-30 15:37:02

282

Views

Uniformly equicontinuous sequence of functions that does not converge uniformly

Published on 30 Dec 2021 - 15:37

score 524 · Answer 13 · 2022-01-13 22:28:39

524

Views

Does a sequence of $C^1$ functions converge to a $C^1$ function if the derivatives are bounded and equicontinuous?

Published on 13 Jan 2022 - 22:28

score 246 · Answer 14 · 2022-02-10 23:00:25

246

Views

Uniform convergence to zero implies equicontinuity

Published on 10 Feb 2022 - 23:00

score 95 · Answer 15 · 2022-02-21 07:57:01

95

Views

If $\{ f_n\}$ is equicontinuous on $X$ and bounded on dense set $D\subseteq X$, then $(f_n)$ is convergent on X.

Published on 21 Feb 2022 - 7:57

List Question

Show that $f_n(x) = x^n$ defines a sequence of equicontinuous functions...

Rudin's PMA Theorem 7.25

Show that F is not equicontinuous

Equivalent condition for equicontinuity of a sequence

Pointwise convergence of $F_n(t) = \max_{y \in \mathbb R^N} \int_{B_t(y)} |u_n|^2 \ dx$

How can we derive the Arzelà-Ascoli theorem for a $\sigma$-compact space from the ordinary Arzelà-Ascoli theorem?

If $(\varphi_n)$ is uniformly equicontinuous and $0\le f_n\le-3\ln\varphi_n$, show that $(f_n)$ is equicontinuous at $0$

Continuous extension in the proof of Arzela - Ascoli theorem

$L^2$ Compactness with the Fourier Transform, Fréchet-Kolmogorov-Riesz theorem

Equicontinuity + pointwise convergence implies uniform continuity

Given a bounded sequence in $L^1([a,b])$, is $(t\mapsto \int_a^t f_n \,\mathrm d\lambda)_n$ equicontinuous?

Uniformly equicontinuous sequence of functions that does not converge uniformly

Does a sequence of $C^1$ functions converge to a $C^1$ function if the derivatives are bounded and equicontinuous?

Uniform convergence to zero implies equicontinuity

If $\{ f_n\}$ is equicontinuous on $X$ and bounded on dense set $D\subseteq X$, then $(f_n)$ is convergent on X.

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