Question

Is the set $S$ of all smooth functions on $B_1$ whose normal derivative vanishes along the boundary $\partial B_1$ dense in $C^0 (B_1, \Bbb C)\ $?

score 120 · Answer 1 · 2026-04-16 07:45:48

120

Views

Is the set $S$ of all smooth functions on $B_1$ whose normal derivative vanishes along the boundary $\partial B_1$ dense in $C^0 (B_1, \Bbb C)\ $?

Published on 16 Apr 2026 - 7:45

score 159 · Answer 2 · 2026-04-15 15:20:41

159

Views

Uniform convergence of $\sum\limits_{n=1}^{\infty} (-1)^n (1-x)x^n$

Published on 15 Apr 2026 - 15:20

score 189 · Answer 3 · 2026-04-14 22:05:32

189

Views

Uniform convergence of $\sum\limits_{n=1}^{\infty} (-1)^n \frac{\arctan(x^n)}{\sqrt{n+1}}$ , $x \in[0,\infty)$

Published on 14 Apr 2026 - 22:05

score 109 · Answer 4 · 2026-04-15 04:09:03

109

Views

Absolute convergence of a telescoping series in a Banach space

Published on 15 Apr 2026 - 4:09

score 364 · Answer 5 · 2026-04-10 19:40:04

364

Views

Convergence of power series with sum of coefficients

Published on 10 Apr 2026 - 19:40

score 70 · Answer 6 · 2026-04-15 08:39:40

70

Views

Convergence on compact sets is equivalent to uniform convergence. Metric spaces.

Published on 15 Apr 2026 - 8:39

score 198 · Answer 7 · 2026-04-12 15:07:53

198

Views

Convergence of a test function sequence

Published on 12 Apr 2026 - 15:07

score 120 · Answer 8 · 2026-04-17 01:18:13

120

Views

Prove convergence of the power series $\sum_{n=1}^\infty \frac{x^n}{\log(n+2)}$

Published on 17 Apr 2026 - 1:18

score 89 · Answer 9 · 2026-04-16 00:41:29

89

Views

Uniform convergence of $f_n(x) = \arctan(nx)$ in the interval $(0,+\infty)$

Published on 16 Apr 2026 - 0:41

score 67 · Answer 10 · 2026-04-16 19:32:24

67

Views

If $f_n \stackrel{\text{unif}}{\longrightarrow} f$, do we have $\int_{0}^{1-1/n} f_n \to \int_0^1 f$ where $f_n \in \mathcal C[0,1]$?

Published on 16 Apr 2026 - 19:32

score 40 · Answer 11 · 2026-04-15 20:04:14

40

Views

Check uniform convergence of a sequence

Published on 15 Apr 2026 - 20:04

score 51 · Answer 12 · 2026-04-16 23:15:53

51

Views

$f_n(x) = \frac{x+x^2}{n}$ is not uniformly convergent

Published on 16 Apr 2026 - 23:15

score 56 · Answer 13 · 2026-04-15 13:24:47

56

Views

If $f_n^2\to f^2$ uniformly, with $f$ and $fn$ being non-negative, does $f_n\to f$ uniformly?

Published on 15 Apr 2026 - 13:24

score 56 · Answer 14 · 2026-04-13 22:44:41

56

Views

Sequence of functions is uniformly convergent to a function (f). Is sequence of their derivatives converging to a derivative (f') at only one point?

Published on 13 Apr 2026 - 22:44

score 38 · Answer 15 · 2026-04-11 20:32:17

38

Views

When does $L_1$ convergence imply compact convergence?

Published on 11 Apr 2026 - 20:32

List Question

Is the set $S$ of all smooth functions on $B_1$ whose normal derivative vanishes along the boundary $\partial B_1$ dense in $C^0 (B_1, \Bbb C)\ $?

Uniform convergence of $\sum\limits_{n=1}^{\infty} (-1)^n (1-x)x^n$

Uniform convergence of $\sum\limits_{n=1}^{\infty} (-1)^n \frac{\arctan(x^n)}{\sqrt{n+1}}$ , $x \in[0,\infty)$

Absolute convergence of a telescoping series in a Banach space

Convergence of power series with sum of coefficients

Convergence on compact sets is equivalent to uniform convergence. Metric spaces.

Convergence of a test function sequence

Prove convergence of the power series $\sum_{n=1}^\infty \frac{x^n}{\log(n+2)}$

Uniform convergence of $f_n(x) = \arctan(nx)$ in the interval $(0,+\infty)$

If $f_n \stackrel{\text{unif}}{\longrightarrow} f$, do we have $\int_{0}^{1-1/n} f_n \to \int_0^1 f$ where $f_n \in \mathcal C[0,1]$?

Check uniform convergence of a sequence

$f_n(x) = \frac{x+x^2}{n}$ is not uniformly convergent

If $f_n^2\to f^2$ uniformly, with $f$ and $fn$ being non-negative, does $f_n\to f$ uniformly?

Sequence of functions is uniformly convergent to a function (f). Is sequence of their derivatives converging to a derivative (f') at only one point?

When does $L_1$ convergence imply compact convergence?

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