Question

How to prove $\sum_{n=0}^{\infty}a_n \cos{(nx)}$ does not uniformly converge in $\left( 0,2\pi \right)$ with the conditions below?

score 112 · Answer 1 · 2023-07-17 17:53:32

112

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How to prove $\sum_{n=0}^{\infty}a_n \cos{(nx)}$ does not uniformly converge in $\left( 0,2\pi \right)$ with the conditions below?

Published on 17 Jul 2023 - 17:53

score 50 · Answer 2 · 2023-07-17 18:13:45

50

Views

$f_n'$ converges uniformly but bounded $f_n$ don't.

Published on 17 Jul 2023 - 18:13

score 174 · Answer 3 · 2023-07-17 18:35:57

174

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What is the usual meaning of this notation $f_n\rightrightarrows f$?

Published on 17 Jul 2023 - 18:35

score 39 · Answer 4 · 2023-07-19 03:59:57

39

Views

Regarding uniform convergence of a series

Published on 19 Jul 2023 - 3:59

score 17 · Answer 5 · 2026-03-31 10:04:23

17

Views

Uniform convergence,continuous functions with a function inside an integral

Published on 31 Mar 2026 - 10:04

score 85 · Answer 6 · 2023-07-19 12:27:36

85

Views

A continuous, almost nowhere differentiable function

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score 242 · Answer 7 · 2023-07-22 15:10:29

242

Views

On a proof of the non-differentiability of the Blancmange curve

Published on 22 Jul 2023 - 15:10

score 53 · Answer 8 · 2023-07-23 10:27:58

53

Views

Determine whether the function $g(x,y) = \sum_{k=1}^\infty \frac{(x-2y)^k \sin(kx + y)}{\sqrt{k!} (1 + x^{2k}y^{4k})}$is continuous on $\mathbb{R}^2$

Published on 23 Jul 2023 - 10:27

score 139 · Answer 9 · 2026-02-23 10:20:47

139

Views

How can we define the supremum norm on the space of continuous functions if they're not necessarily bounded?

Published on 23 Feb 2026 - 10:20

score 58 · Answer 10 · 2026-02-24 17:13:17

58

Views

Pointwise convergence of a function where convergence to multiple values occur at a single point

Published on 24 Feb 2026 - 17:13

score 79 · Answer 11 · 2026-02-25 02:28:12

79

Views

Rudin $7.14$ linked to $7.9$ why does Rudin make boundedness compulsory in uniform convergence?

Published on 25 Feb 2026 - 2:28

score 67 · Answer 12 · 2026-04-03 03:28:09

67

Views

Partial sums of the Riemann zeta function and uniform convergence

Published on 03 Apr 2026 - 3:28

score 104 · Answer 13 · 2026-03-31 07:56:48

104

Views

Prove that the Bernstein polynomials converge uniformly

Published on 31 Mar 2026 - 7:56

score 75 · Answer 14 · 2023-07-30 05:15:55

75

Views

Trouble proving $\lim_{n\to\infty} x^n=0$ when $|x|<1$.

Published on 30 Jul 2023 - 5:15

score 67 · Answer 15 · 2023-07-30 15:50:46

67

Views

Uniform convergence implies convergence in expectation, Lebesgue integral

Published on 30 Jul 2023 - 15:50

List Question

How to prove $\sum_{n=0}^{\infty}a_n \cos{(nx)}$ does not uniformly converge in $\left( 0,2\pi \right)$ with the conditions below?

$f_n'$ converges uniformly but bounded $f_n$ don't.

What is the usual meaning of this notation $f_n\rightrightarrows f$?

Regarding uniform convergence of a series

Uniform convergence,continuous functions with a function inside an integral

A continuous, almost nowhere differentiable function

On a proof of the non-differentiability of the Blancmange curve

Determine whether the function $g(x,y) = \sum_{k=1}^\infty \frac{(x-2y)^k \sin(kx + y)}{\sqrt{k!} (1 + x^{2k}y^{4k})}$is continuous on $\mathbb{R}^2$

How can we define the supremum norm on the space of continuous functions if they're not necessarily bounded?

Pointwise convergence of a function where convergence to multiple values occur at a single point

Rudin $7.14$ linked to $7.9$ why does Rudin make boundedness compulsory in uniform convergence?

Partial sums of the Riemann zeta function and uniform convergence

Prove that the Bernstein polynomials converge uniformly

Trouble proving $\lim_{n\to\infty} x^n=0$ when $|x|<1$.

Uniform convergence implies convergence in expectation, Lebesgue integral

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