List questions from uniform-convergence

Published on 13 Apr 2026 - 23:08

109

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Does weak convergence in $L^2$ plus uniform convergence imply strong convergence in $L^2$?

Published on 13 Apr 2026 - 21:12

59

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why $1+\sqrt{n}|x|^2 \ge 2\sqrt{n}|x|?$ why not $1+\sqrt{n}|x|^2 \ge 2\sqrt{n}|x|^2?$

Published on 17 Apr 2026 - 4:58

84

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$2^{-n}\varphi(x/n) $ does not converge in $\mathscr{D}(\mathbb{R}^n)$

Published on 14 Apr 2026 - 16:39

105

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$f_n(t)=\int_{-n}^{n} \frac{\sin x}{x}\cdot e^{-itx}\ dx$ converges uniformly near $t=0$.

Published on 28 Apr 2026 - 12:33

223

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Pointwise convergence of Fourier Series to aperiodic function

Published on 11 Apr 2026 - 10:23

180

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Uniform convergence of a sequence of operators

Published on 16 Apr 2026 - 7:38

68

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Uniform convergence and translation

Published on 16 Apr 2026 - 5:40

571

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Show that $f_n(x) = x^n$ defines a sequence of equicontinuous functions...

Published on 11 Apr 2026 - 23:30

101

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Uniform Convergence of Electric Field Integral

Published on 13 Apr 2026 - 20:07

34

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Sequence of functions versus sequence of integrals of functions: uniform convergence

Published on 17 Apr 2026 - 9:57

79

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Show that limit function exists and evaluate the limit function

Published on 14 Apr 2026 - 10:22

74

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Strong Law of Large Numbers without assuming $\Bbb{E} X^2 < \infty$

Published on 12 Apr 2026 - 18:31

107

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Prove that there exists $n_0 \in \mathbb N$ such that $\sum\limits_{n = n_0+1}^{\infty} \log (1 + g_n (x))$ converges absolutely and uniformly on $X.$

Published on 17 Apr 2026 - 23:52

157

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Does $nx^n(1-x^2)$ converges uniformly to $0$ on $[0,1]$?

Published on 17 Apr 2026 - 23:38

List Question

Exercise about $\sum_{n=1}^{\infty}\frac{e^{-nx}}{n+1}$

Does weak convergence in $L^2$ plus uniform convergence imply strong convergence in $L^2$?

why $1+\sqrt{n}|x|^2 \ge 2\sqrt{n}|x|?$ why not $1+\sqrt{n}|x|^2 \ge 2\sqrt{n}|x|^2?$

$2^{-n}\varphi(x/n) $ does not converge in $\mathscr{D}(\mathbb{R}^n)$

$f_n(t)=\int_{-n}^{n} \frac{\sin x}{x}\cdot e^{-itx}\ dx$ converges uniformly near $t=0$.

Pointwise convergence of Fourier Series to aperiodic function

Uniform convergence of a sequence of operators

Uniform convergence and translation

Show that $f_n(x) = x^n$ defines a sequence of equicontinuous functions...

Uniform Convergence of Electric Field Integral

Sequence of functions versus sequence of integrals of functions: uniform convergence

Show that limit function exists and evaluate the limit function

Strong Law of Large Numbers without assuming $\Bbb{E} X^2 < \infty$

Prove that there exists $n_0 \in \mathbb N$ such that $\sum\limits_{n = n_0+1}^{\infty} \log (1 + g_n (x))$ converges absolutely and uniformly on $X.$

Does $nx^n(1-x^2)$ converges uniformly to $0$ on $[0,1]$?

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