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Confusion about "$:=$" notation in pointwise convergence definition

score 84 · Answer 1 · 2023-11-03 19:07:45

84

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Confusion about "$:=$" notation in pointwise convergence definition

Published on 03 Nov 2023 - 19:07

score 75 · Answer 2 · 2023-11-09 10:36:38

75

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Does the sum of a sequence of functions $\{f_n(x)\}$ converge if the upper bound $h_n(x)$ with $f_n(x)\le h_n(x)$ converges pointwise to $0$?

Published on 09 Nov 2023 - 10:36

score 117 · Answer 3 · 2023-11-15 02:56:04

117

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Questions and observations regarding Putnam 2020 - A.6.

Published on 15 Nov 2023 - 2:56

score 83 · Answer 4 · 2023-11-17 19:13:45

83

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Proving that the infinite sum converges to $1$ as $k$ tends to infinity

Published on 17 Nov 2023 - 19:13

score 160 · Answer 5 · 2023-11-30 02:43:54

160

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Proving that convergence in RKHS implies pointwise convergence without using reproducing property

Published on 30 Nov 2023 - 2:43

score 65 · Answer 6 · 2023-12-06 10:11:56

65

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Convergence of $f_n(x) = \frac{\sqrt x (1-x)}{1+nx}$ and $g_n(x) = \sqrt n f_n(x)$

Published on 06 Dec 2023 - 10:11

score 22 · Answer 7 · 2023-12-08 20:24:45

22

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Pointwise ad unifrom convergence of $g_n : \mathbb R \times \mathbb R^+ \to \mathbb R$.

Published on 08 Dec 2023 - 20:24

score 47 · Answer 8 · 2023-12-14 04:47:27

47

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Some Locally Uniform Convergence

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score 28 · Answer 9 · 2023-12-16 13:05:44

28

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Proving numerical method 1st-order convergence

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score 94 · Answer 10 · 2023-12-16 19:04:25

94

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Whats the point of Pointwise Convergence

Published on 16 Dec 2023 - 19:04

score 43 · Answer 11 · 2023-12-21 16:30:47

43

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Show the sequence of functions (which can graphically be described as shrinking width triangles of height 1) converges pointwise to the zero function.

Published on 21 Dec 2023 - 16:30

score 86 · Answer 12 · 2023-12-22 13:44:10

86

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Does fourier series for $f(x)=\begin{cases}-1\ \text{for}\ x \in (-\pi, 0) \\0 \ \text{for}\ x=0 \\ 1 \ \text{for} \ x\in (0,\pi)\end{cases}$ converge

Published on 22 Dec 2023 - 13:44

score 79 · Answer 13 · 2024-01-04 19:50:27

79

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How to show that the series of functions $\sum_{k = 0}^\infty(-1)^k \frac{x^{2k + 1}}{2k + 1}$ is pointwise convergent to a function?

Published on 04 Jan 2024 - 19:50

score 52 · Answer 14 · 2024-01-06 23:45:11

52

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Convergence of a series of the product of two functions when one of them is shifted by one

Published on 06 Jan 2024 - 23:45

score 40 · Answer 15 · 2024-01-09 00:21:23

40

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Question on pointwise convergence and norms

Published on 09 Jan 2024 - 0:21

List Question

Confusion about "$:=$" notation in pointwise convergence definition

Does the sum of a sequence of functions $\{f_n(x)\}$ converge if the upper bound $h_n(x)$ with $f_n(x)\le h_n(x)$ converges pointwise to $0$?

Questions and observations regarding Putnam 2020 - A.6.

Proving that the infinite sum converges to $1$ as $k$ tends to infinity

Proving that convergence in RKHS implies pointwise convergence without using reproducing property

Convergence of $f_n(x) = \frac{\sqrt x (1-x)}{1+nx}$ and $g_n(x) = \sqrt n f_n(x)$

Pointwise ad unifrom convergence of $g_n : \mathbb R \times \mathbb R^+ \to \mathbb R$.

Some Locally Uniform Convergence

Proving numerical method 1st-order convergence

Whats the point of Pointwise Convergence

Show the sequence of functions (which can graphically be described as shrinking width triangles of height 1) converges pointwise to the zero function.

Does fourier series for $f(x)=\begin{cases}-1\ \text{for}\ x \in (-\pi, 0) \\0 \ \text{for}\ x=0 \\ 1 \ \text{for} \ x\in (0,\pi)\end{cases}$ converge

How to show that the series of functions $\sum_{k = 0}^\infty(-1)^k \frac{x^{2k + 1}}{2k + 1}$ is pointwise convergent to a function?

Convergence of a series of the product of two functions when one of them is shifted by one

Question on pointwise convergence and norms

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