Question

Why does the mollified function converge uniformly to the original $W^{1,\infty}$ function

score 783 · Answer 1 · 2026-04-12 07:09:44

783

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Why does the mollified function converge uniformly to the original $W^{1,\infty}$ function

Published on 12 Apr 2026 - 7:09

score 89 · Answer 2 · 2015-09-25 08:53:51

89

Views

$f:[a,b]\to \mathbb R$ be Riemann Integrable , then $g_n(x):= \int _a^x f(t)\cos(nt)dt$ converges uniformly , on $[a,b]$ , to the zero function ?

Published on 25 Sep 2015 - 8:53

score 631 · Answer 3 · 2026-04-01 09:55:35

631

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Examples that the conclusion of Arzela-Ascoli does not follow when equicontinuity or uniform boundedness is dropped?

Published on 01 Apr 2026 - 9:55

score 2.8k · Answer 4 · 2015-09-26 19:17:29

2.8k

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If $\sum A_n$ converges, does $\sum A_n x^n$ converge uniformly on $[0,1]$?

Published on 26 Sep 2015 - 19:17

score 1.1k · Answer 5 · 2026-04-10 14:36:24

1.1k

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An application of Arzelà Ascoli theorem

Published on 10 Apr 2026 - 14:36

score 694 · Answer 6 · 2015-09-26 20:00:41

694

Views

Construct a sequence of functions which is pointwise convergent to zero and not uniformly convergent on any interval.

Published on 26 Sep 2015 - 20:00

score 335 · Answer 7 · 2026-04-12 21:04:09

335

Views

Uniform convergence of a sequence of functions?

Published on 12 Apr 2026 - 21:04

score 154 · Answer 8 · 2015-10-02 07:54:43

154

Views

Find a sequence of differentiable functions $\{f_n\}$ on $[0,1]$ such that $f_n \to 0$ uniformly, but $\{f_n'(1/2)\}$ does not converge to $0$.

Published on 02 Oct 2015 - 7:54

score 3.5k · Answer 9 · 2015-10-02 16:05:12

A sequence of differentiable functions that converge uniformly to a non differentiable function - is my example correct?

score 58 · Answer 10 · 2015-10-02 16:10:51

58

Views

uniform convergence of $u(\sigma,t)=\frac{1}{\pi}\int_{-\infty}^{\infty}{f(t+\sigma u)\frac{du}{1+u^2}}$ as $\sigma$ goes to zero

Published on 02 Oct 2015 - 16:10

score 169 · Answer 11 · 2015-10-02 18:36:21

169

Views

Series converging uniformly in a subset of the unit disc

Published on 02 Oct 2015 - 18:36

score 1k · Answer 12 · 2015-10-03 13:43:01

1k

Views

Show that $(1+\frac{x}{n})^n e^{-x} \rightarrow 1$ converges uniformly.

Published on 03 Oct 2015 - 13:43

score 370 · Answer 13 · 2015-10-03 18:42:31

370

Views

Does $f_n\rightarrow f$ uniformly suggest $\sum f_n\rightarrow\sum f$ uniformly?

Published on 03 Oct 2015 - 18:42

score 142 · Answer 14 · 2026-04-11 17:02:03

142

Views

Proof that asymptotic approximation on interval plus monotonicity (decreasing) implies uniformity?

Published on 11 Apr 2026 - 17:02

score 70 · Answer 15 · 2026-04-12 01:05:14

70

Views

Can we express uniform continuity in terms of uniform convergence?

Published on 12 Apr 2026 - 1:05

List Question

Why does the mollified function converge uniformly to the original $W^{1,\infty}$ function

$f:[a,b]\to \mathbb R$ be Riemann Integrable , then $g_n(x):= \int _a^x f(t)\cos(nt)dt$ converges uniformly , on $[a,b]$ , to the zero function ?

Examples that the conclusion of Arzela-Ascoli does not follow when equicontinuity or uniform boundedness is dropped?

If $\sum A_n$ converges, does $\sum A_n x^n$ converge uniformly on $[0,1]$?

An application of Arzelà Ascoli theorem

Construct a sequence of functions which is pointwise convergent to zero and not uniformly convergent on any interval.

Uniform convergence of a sequence of functions?

Find a sequence of differentiable functions $\{f_n\}$ on $[0,1]$ such that $f_n \to 0$ uniformly, but $\{f_n'(1/2)\}$ does not converge to $0$.

A sequence of differentiable functions that converge uniformly to a non differentiable function - is my example correct?

uniform convergence of $u(\sigma,t)=\frac{1}{\pi}\int_{-\infty}^{\infty}{f(t+\sigma u)\frac{du}{1+u^2}}$ as $\sigma$ goes to zero

Series converging uniformly in a subset of the unit disc

Show that $(1+\frac{x}{n})^n e^{-x} \rightarrow 1$ converges uniformly.

Does $f_n\rightarrow f$ uniformly suggest $\sum f_n\rightarrow\sum f$ uniformly?

Proof that asymptotic approximation on interval plus monotonicity (decreasing) implies uniformity?

Can we express uniform continuity in terms of uniform convergence?

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