Question

Proving local uniform convergence of a series of functions

score 59 · Answer 1 · 2026-04-15 08:01:11

59

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Proving local uniform convergence of a series of functions

Published on 15 Apr 2026 - 8:01

score 87 · Answer 2 · 2026-04-08 11:41:34

87

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Stone Weirstrass proof clarification

Published on 08 Apr 2026 - 11:41

score 91 · Answer 3 · 2026-04-15 01:11:24

91

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Show that $f_n$ does not converge to $f$ in the uniform norm but does converge on the norm $||f||=\sqrt{\int_a^b|f(x)|^2}dx$

Published on 15 Apr 2026 - 1:11

score 74 · Answer 4 · 2026-04-15 21:38:28

74

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Show that if the series $\sum_{n=1}^\infty f_n$ is uniformly convergent on $\Bbb R$, then the sequence $(f_n)$ converges to $0$ on $\Bbb R$.

Published on 15 Apr 2026 - 21:38

score 48 · Answer 5 · 2026-04-14 23:23:49

48

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Investigate whether the series $\sum_{n=1}^\infty \frac{1+x^2 \sin (5x)}{\sqrt{n^3}}$ converges uniformly on $[-4,2]$ or not.

Published on 14 Apr 2026 - 23:23

score 103 · Answer 6 · 2026-04-16 23:48:34

103

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Where exactly does the series of functions $\sum_{n = 1}^{\infty} \frac{1}{n^2 (x+1)}$ converge uniformly?

Published on 16 Apr 2026 - 23:48

score 57 · Answer 7 · 2026-04-17 02:51:27

$f_n(x) =\frac{n}{2}\left(e^{\left(\frac{1}{n}-4\right)x}-e^{\left(-\frac{1}{n}-4\right)x}\right)$ - Prove uniform convergence in $[-1,1]$

score 121 · Answer 8 · 2026-04-12 13:27:20

121

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why is the Laplace transform of local integrable function with support on $[0,\infty)$ analytic?

Published on 12 Apr 2026 - 13:27

score 188 · Answer 9 · 2026-04-15 11:37:35

188

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Prove that countable intersection/union of zero/cozero sets is a zero/cozero set.

Published on 15 Apr 2026 - 11:37

score 71 · Answer 10 · 2026-04-19 05:49:36

71

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Almost uniform convergence on an open set, pointwise convergence on a closed set and an equality of a limit of an integral of the sequence to examine.

Published on 19 Apr 2026 - 5:49

score 93 · Answer 11 · 2026-04-12 05:42:49

93

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$L_\infty$ norm and uniform convergence with Lebesgue integral

Published on 12 Apr 2026 - 5:42

score 97 · Answer 12 · 2026-04-21 15:46:13

97

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Sequence of functions $(f_n)$ with $|f_{n+1}(x)-f_n(x)| \le \frac{1}{2^n+x^2}$ is uniformly convergent in $\Bbb R$

Published on 21 Apr 2026 - 15:46

score 232 · Answer 13 · 2026-04-16 13:16:45

232

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Uniform convergence of $\{f_n\}$ satisfying $f_n\left(x + \frac{1}{n}\right) = f_n(x)$ implies that the limit is a constant function

Published on 16 Apr 2026 - 13:16

score 120 · Answer 14 · 2026-04-16 12:11:56

120

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Prove that $f_n(x) = \frac{nx}{1+n^2x^2}$ is not uniformly convergent on any interval containing $0$.

Published on 16 Apr 2026 - 12:11

score 66 · Answer 15 · 2026-04-14 22:26:53

66

Views

Arzelà–Ascoli propagation theorem

Published on 14 Apr 2026 - 22:26

List Question

Proving local uniform convergence of a series of functions

Stone Weirstrass proof clarification

Show that $f_n$ does not converge to $f$ in the uniform norm but does converge on the norm $||f||=\sqrt{\int_a^b|f(x)|^2}dx$

Show that if the series $\sum_{n=1}^\infty f_n$ is uniformly convergent on $\Bbb R$, then the sequence $(f_n)$ converges to $0$ on $\Bbb R$.

Investigate whether the series $\sum_{n=1}^\infty \frac{1+x^2 \sin (5x)}{\sqrt{n^3}}$ converges uniformly on $[-4,2]$ or not.

Where exactly does the series of functions $\sum_{n = 1}^{\infty} \frac{1}{n^2 (x+1)}$ converge uniformly?

$f_n(x) =\frac{n}{2}\left(e^{\left(\frac{1}{n}-4\right)x}-e^{\left(-\frac{1}{n}-4\right)x}\right)$ - Prove uniform convergence in $[-1,1]$

why is the Laplace transform of local integrable function with support on $[0,\infty)$ analytic?

Prove that countable intersection/union of zero/cozero sets is a zero/cozero set.

Almost uniform convergence on an open set, pointwise convergence on a closed set and an equality of a limit of an integral of the sequence to examine.

$L_\infty$ norm and uniform convergence with Lebesgue integral

Sequence of functions $(f_n)$ with $|f_{n+1}(x)-f_n(x)| \le \frac{1}{2^n+x^2}$ is uniformly convergent in $\Bbb R$

Uniform convergence of $\{f_n\}$ satisfying $f_n\left(x + \frac{1}{n}\right) = f_n(x)$ implies that the limit is a constant function

Prove that $f_n(x) = \frac{nx}{1+n^2x^2}$ is not uniformly convergent on any interval containing $0$.

Arzelà–Ascoli propagation theorem

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