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Exercise about pointwise and uniform convergence

score 380 · Answer 1 · 2026-05-15 09:24:03

380

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Exercise about pointwise and uniform convergence

Published on 15 May 2026 - 9:24

score 96 · Answer 2 · 2026-04-17 06:28:14

96

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Show that the set $P=\{f\in X:f$ is a polynomial$\}$ is dense in $X$.

Published on 17 Apr 2026 - 6:28

score 431 · Answer 3 · 2026-05-11 00:56:50

431

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If a seq of holomorphic function on an open set $\Omega$, $\{f_n\}$ coverges uniformly to a function $f$ on every compact set then so does $f_n'$

Published on 11 May 2026 - 0:56

score 58 · Answer 4 · 2026-04-16 20:06:01

58

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For $f_n \in C^\infty (\mathbb{R})$, prove $xf_n(x) \to 0$ uniformly given some conditions on all derivatives.

Published on 16 Apr 2026 - 20:06

score 67 · Answer 5 · 2026-04-11 13:36:50

67

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is $f_n=x^{-n} $convergent point wise? uniformly?

Published on 11 Apr 2026 - 13:36

score 24 · Answer 6 · 2026-04-13 23:20:30

24

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Uniform Convergence Implied By Converging Sum

Published on 13 Apr 2026 - 23:20

score 69 · Answer 7 · 2026-04-16 12:33:53

69

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define uniform convergence of this function: $fn(x)=n.x.(1-x)^n$

Published on 16 Apr 2026 - 12:33

score 28 · Answer 8 · 2026-04-11 13:31:36

28

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Does taking the limit in one argument preserve regularity in another argument?

Published on 11 Apr 2026 - 13:31

score 76 · Answer 9 · 2026-04-12 08:31:20

76

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Problem in showing convergence in almost uniformly on finite measure set implies Convergence in $L^2$ measure

Published on 12 Apr 2026 - 8:31

score 22 · Answer 10 · 2026-04-09 05:40:49

22

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Fourier sine series of piece wise defined function

Published on 09 Apr 2026 - 5:40

score 379 · Answer 11 · 2026-04-13 22:42:59

379

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When does Almost sure convergence imply Almost sure uniform convergence?

Published on 13 Apr 2026 - 22:42

score 49 · Answer 12 · 2026-05-15 17:07:13

49

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proof verification: Proving an upper bound for a uniformly convergent sequence of functions on $\mathbb{R}$

Published on 15 May 2026 - 17:07

score 58 · Answer 13 · 2026-04-15 17:14:11

58

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Uniform convergence of the series with sin

Published on 15 Apr 2026 - 17:14

score 161 · Answer 14 · 2026-05-15 19:07:26

161

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Uniform Convergence and continuity (Rudin 7.4)

Published on 15 May 2026 - 19:07

score 62 · Answer 15 · 2026-04-15 20:25:45

62

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Uniform Convergence of $\sum_1^\infty(-x)^n/n$ on $[a, 1]$

Published on 15 Apr 2026 - 20:25

List Question

Exercise about pointwise and uniform convergence

Show that the set $P=\{f\in X:f$ is a polynomial$\}$ is dense in $X$.

If a seq of holomorphic function on an open set $\Omega$, $\{f_n\}$ coverges uniformly to a function $f$ on every compact set then so does $f_n'$

For $f_n \in C^\infty (\mathbb{R})$, prove $xf_n(x) \to 0$ uniformly given some conditions on all derivatives.

is $f_n=x^{-n} $convergent point wise? uniformly?

Uniform Convergence Implied By Converging Sum

define uniform convergence of this function: $fn(x)=n.x.(1-x)^n$

Does taking the limit in one argument preserve regularity in another argument?

Problem in showing convergence in almost uniformly on finite measure set implies Convergence in $L^2$ measure

Fourier sine series of piece wise defined function

When does Almost sure convergence imply Almost sure uniform convergence?

proof verification: Proving an upper bound for a uniformly convergent sequence of functions on $\mathbb{R}$

Uniform convergence of the series with sin

Uniform Convergence and continuity (Rudin 7.4)

Uniform Convergence of $\sum_1^\infty(-x)^n/n$ on $[a, 1]$

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