Question

Let $(f_n)\to 0$ uniformly and $|\sum g_n|<\infty$. Prove that $\sum f_n g_n$ converges uniformly.

score 533 · Answer 1 · 2017-01-27 22:13:41

533

Views

Let $(f_n)\to 0$ uniformly and $|\sum g_n|<\infty$. Prove that $\sum f_n g_n$ converges uniformly.

Published on 27 Jan 2017 - 22:13

score 364 · Answer 2 · 2017-01-29 01:19:54

364

Views

Uniform Convergence of sequence of derivatives

Published on 29 Jan 2017 - 1:19

score 774 · Answer 3 · 2026-02-23 08:53:10

774

Views

Does this function sequence have a convergent subsequence?

Published on 23 Feb 2026 - 8:53

score 262 · Answer 4 · 2026-03-21 23:46:21

262

Views

Could you please help give a hint to solve this problem in real analysis (uniform convergence)?

Published on 21 Mar 2026 - 23:46

score 331 · Answer 5 · 2017-01-30 01:58:31

331

Views

$f_n(x)=\frac{x^2}{x^2+n}$ does not converge uniformly on $\mathbb{R}$, but it converges uniformly on any bounded subset $E$

Published on 30 Jan 2017 - 1:58

score 411 · Answer 6 · 2017-01-30 02:19:58

411

Views

Show that the sequence of functions ${f_n}(x)=\frac{x}{1+nx^2}$ converges uniformly

Published on 30 Jan 2017 - 2:19

score 5.7k · Answer 7 · 2017-01-30 13:43:22

5.7k

Views

x/n uniformly convergent?

Published on 30 Jan 2017 - 13:43

score 87 · Answer 8 · 2017-01-30 23:32:07

87

Views

Pointwise and uniform convergence difference

Published on 30 Jan 2017 - 23:32

score 1.9k · Answer 9 · 2017-01-31 21:14:47

1.9k

Views

If $\sum g_n$ converges uniformly , then does $(g_n)$ converge uniformly to $0$?

Published on 31 Jan 2017 - 21:14

score 45 · Answer 10 · 2017-02-01 12:49:57

45

Views

Two questions on uniform convergence

Published on 01 Feb 2017 - 12:49

score 533 · Answer 11 · 2017-02-01 23:42:00

533

Views

On the uniform convergence of series of functions with indexes in $\mathbb{Z}$

Published on 01 Feb 2017 - 23:42

score 212 · Answer 12 · 2017-02-02 02:34:04

212

Views

Uniform Convergence of Sequence of Functions and their derivatives

Published on 02 Feb 2017 - 2:34

score 276 · Answer 13 · 2017-02-02 13:03:24

276

Views

Uniform convergence of a pointwise convergent series of function converging uniformly to zero

Published on 02 Feb 2017 - 13:03

score 3.6k · Answer 14 · 2026-03-30 13:53:48

3.6k

Views

How to prove that $f(x)=e^{x}$ is not a polynomial.

Published on 30 Mar 2026 - 13:53

score 39 · Answer 15 · 2017-02-03 17:09:25

39

Views

It's true that $\sum_{k\in \mathbb N}|f ^{(k)}|_X < \infty$?

Published on 03 Feb 2017 - 17:09

List Question

Let $(f_n)\to 0$ uniformly and $|\sum g_n|<\infty$. Prove that $\sum f_n g_n$ converges uniformly.

Uniform Convergence of sequence of derivatives

Does this function sequence have a convergent subsequence?

Could you please help give a hint to solve this problem in real analysis (uniform convergence)?

$f_n(x)=\frac{x^2}{x^2+n}$ does not converge uniformly on $\mathbb{R}$, but it converges uniformly on any bounded subset $E$

Show that the sequence of functions ${f_n}(x)=\frac{x}{1+nx^2}$ converges uniformly

x/n uniformly convergent?

Pointwise and uniform convergence difference

If $\sum g_n$ converges uniformly , then does $(g_n)$ converge uniformly to $0$?

Two questions on uniform convergence

On the uniform convergence of series of functions with indexes in $\mathbb{Z}$

Uniform Convergence of Sequence of Functions and their derivatives

Uniform convergence of a pointwise convergent series of function converging uniformly to zero

How to prove that $f(x)=e^{x}$ is not a polynomial.

It's true that $\sum_{k\in \mathbb N}|f ^{(k)}|_X < \infty$?

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