Question

Absolute convergence and continuity imply uniform convergence of Fourier series to the function?

score 688 · Answer 1 · 2026-03-26 12:37:57

688

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Absolute convergence and continuity imply uniform convergence of Fourier series to the function?

Published on 26 Mar 2026 - 12:37

score 2.3k · Answer 2 · 2026-04-06 19:08:09

2.3k

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Convergence in compact-open topology implies uniform convergence on compacts

Published on 06 Apr 2026 - 19:08

score 633 · Answer 3 · 2016-07-28 00:13:46

633

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Uniform Convergence of the series $f(x)=\sum_{n=1}^{\infty} \frac{(\cos nx)^{n^2}}{(e^x+x)^n}$

Published on 28 Jul 2016 - 0:13

score 124 · Answer 4 · 2016-07-29 18:10:55

124

Views

Proving uniform convergence of $\{f_n\}$ under some conditions on $\{f_n'\}$

Published on 29 Jul 2016 - 18:10

score 1.8k · Answer 5 · 2026-02-24 21:35:37

1.8k

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Showing that $f_n(x) = \frac{nx}{1+n^2x^2}$ does not converge uniformly

Published on 24 Feb 2026 - 21:35

score 173 · Answer 6 · 2026-04-04 10:39:44

173

Views

Definitions of locally uniform convergence in Banach spaces

Published on 04 Apr 2026 - 10:39

score 6.3k · Answer 7 · 2016-07-30 15:15:29

6.3k

Views

Uniform Convergence of Power Series

Published on 30 Jul 2016 - 15:15

score 50 · Answer 8 · 2016-08-02 10:15:12

50

Views

sequence of functions-convergence

Published on 02 Aug 2016 - 10:15

score 69 · Answer 9 · 2016-08-02 19:17:56

69

Views

Clarification needed regarding uniform convergence of a sequence of functions

Published on 02 Aug 2016 - 19:17

score 51 · Answer 10 · 2016-08-07 01:07:20

51

Views

Clarification on Uniform Convergence (and some properties)

Published on 07 Aug 2016 - 1:07

score 530 · Answer 11 · 2026-03-29 10:37:11

530

Views

Product space, product and uniform topology -- open sets?

Published on 29 Mar 2026 - 10:37

score 89 · Answer 12 · 2016-08-10 05:01:20

89

Views

Proof check that $\int\limits_0^1\left(\sum\limits_{k=0}^\infty a_kx^k\right)dx=\sum\limits_{k=0}^\infty\frac{a_k}{k+1}$

Published on 10 Aug 2016 - 5:01

score 418 · Answer 13 · 2016-08-12 01:26:39

418

Views

Can Dini's theorem be strengthened to allow "pointwise" monotonicity?

Published on 12 Aug 2016 - 1:26

score 582 · Answer 14 · 2016-08-12 06:47:31

582

Views

uniform boundedness + $f_n, f$ continuous + $f_n\to f$ on compact set $\implies$ uniform convergence?

Published on 12 Aug 2016 - 6:47

score 496 · Answer 15 · 2016-08-15 17:41:16

496

Views

Can we interchange limits for weak convergence of double sequences?

Published on 15 Aug 2016 - 17:41

List Question

Absolute convergence and continuity imply uniform convergence of Fourier series to the function?

Convergence in compact-open topology implies uniform convergence on compacts

Uniform Convergence of the series $f(x)=\sum_{n=1}^{\infty} \frac{(\cos nx)^{n^2}}{(e^x+x)^n}$

Proving uniform convergence of $\{f_n\}$ under some conditions on $\{f_n'\}$

Showing that $f_n(x) = \frac{nx}{1+n^2x^2}$ does not converge uniformly

Definitions of locally uniform convergence in Banach spaces

Uniform Convergence of Power Series

sequence of functions-convergence

Clarification needed regarding uniform convergence of a sequence of functions

Clarification on Uniform Convergence (and some properties)

Product space, product and uniform topology -- open sets?

Proof check that $\int\limits_0^1\left(\sum\limits_{k=0}^\infty a_kx^k\right)dx=\sum\limits_{k=0}^\infty\frac{a_k}{k+1}$

Can Dini's theorem be strengthened to allow "pointwise" monotonicity?

uniform boundedness + $f_n, f$ continuous + $f_n\to f$ on compact set $\implies$ uniform convergence?

Can we interchange limits for weak convergence of double sequences?

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