Question

Derivative Properties of the Limit of a ‘Cyclodifferential’ Function Series

score 27 · Answer 1 · 2023-06-07 16:10:28

27

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Derivative Properties of the Limit of a ‘Cyclodifferential’ Function Series

Published on 07 Jun 2023 - 16:10

score 62 · Answer 2 · 2023-06-11 00:32:23

62

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Does $\sum_{n=1}^{\infty} \frac{1}{n^3 x + \sqrt[3]{n} }$ uniformly converge on $A = (0, + \infty)$

Published on 11 Jun 2023 - 0:32

score 70 · Answer 3 · 2023-06-12 18:29:10

70

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Continuous convergence: If $f_n \to f$ continously and $x_n \to x$, then does $f_{a_n}(x_n) \to f(x)$ where $a_n \to \infty$.

Published on 12 Jun 2023 - 18:29

score 246 · Answer 4 · 2023-06-13 13:05:22

246

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Prove uniform convergence point by point?

Published on 13 Jun 2023 - 13:05

score 205 · Answer 5 · 2023-06-15 15:56:58

205

Views

Approximating continuous functions with compact support by simple functions in $L^\infty$ norm

Published on 15 Jun 2023 - 15:56

score 94 · Answer 6 · 2023-06-15 23:42:40

If $U_n \to U$ locally uniformly, and $g \colon \mathbb{R} \to \mathbb{R} $ is continuous and bounded, $gU_n \to gU$ locally uniformly.

score 70 · Answer 7 · 2023-06-16 10:41:28

70

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Does $f_n = n \chi_{[0,\frac{1}{n}]} \to 0$ almost uniformly?

Published on 16 Jun 2023 - 10:41

score 63 · Answer 8 · 2026-02-23 04:20:09

63

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The conditions under which a function family becomes a normal family - complex analysis

Published on 23 Feb 2026 - 4:20

score 84 · Answer 9 · 2026-02-25 02:26:28

84

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Uniform convergence, functions,sequences,subsequences

Published on 25 Feb 2026 - 2:26

score 32 · Answer 10 · 2026-03-31 03:26:51

32

Views

Uniform limit theorem for arbitrary uniform space.

Published on 31 Mar 2026 - 3:26

score 121 · Answer 11 · 2026-02-25 02:28:12

121

Views

Examples of spaces where compact convergence is not equivalent to local uniform convergence.

Published on 25 Feb 2026 - 2:28

score 93 · Answer 12 · 2023-06-21 04:33:21

93

Views

Check if $f_n(x)=\begin{cases} 1-\frac{1}{n}|x| & \text{ if } |x|< n \\ 0& \text{ if } |x|\geq n \end{cases}$ uniformly converges to $f=1$

Published on 21 Jun 2023 - 4:33

score 154 · Answer 13 · 2026-02-25 02:31:48

154

Views

check uniformly convergence of $f_n(x)=\begin{cases} nx & \text{ if } 0\leq x \leq \frac{1}{n}\\1& \text{ if } \frac{1}{n}<x\leq 1\\ \end{cases}$

Published on 25 Feb 2026 - 2:31

score 58 · Answer 14 · 2026-03-30 16:01:48

58

Views

Cauchy sequences continuity,Uniform Continuity

Published on 30 Mar 2026 - 16:01

score 108 · Answer 15 · 2026-02-25 02:28:49

108

Views

Check that $\sum_{n=0}^{\infty}(1-x^2)x^n$ uniformly converges on $[0;1]$

Published on 25 Feb 2026 - 2:28

List Question

Derivative Properties of the Limit of a ‘Cyclodifferential’ Function Series

Does $\sum_{n=1}^{\infty} \frac{1}{n^3 x + \sqrt[3]{n} }$ uniformly converge on $A = (0, + \infty)$

Continuous convergence: If $f_n \to f$ continously and $x_n \to x$, then does $f_{a_n}(x_n) \to f(x)$ where $a_n \to \infty$.

Prove uniform convergence point by point?

Approximating continuous functions with compact support by simple functions in $L^\infty$ norm

If $U_n \to U$ locally uniformly, and $g \colon \mathbb{R} \to \mathbb{R} $ is continuous and bounded, $gU_n \to gU$ locally uniformly.

Does $f_n = n \chi_{[0,\frac{1}{n}]} \to 0$ almost uniformly?

The conditions under which a function family becomes a normal family - complex analysis

Uniform convergence, functions,sequences,subsequences

Uniform limit theorem for arbitrary uniform space.

Examples of spaces where compact convergence is not equivalent to local uniform convergence.

Check if $f_n(x)=\begin{cases} 1-\frac{1}{n}|x| & \text{ if } |x|< n \\ 0& \text{ if } |x|\geq n \end{cases}$ uniformly converges to $f=1$

check uniformly convergence of $f_n(x)=\begin{cases} nx & \text{ if } 0\leq x \leq \frac{1}{n}\\1& \text{ if } \frac{1}{n}<x\leq 1\\ \end{cases}$

Cauchy sequences continuity,Uniform Continuity

Check that $\sum_{n=0}^{\infty}(1-x^2)x^n$ uniformly converges on $[0;1]$

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