Question

Let $M=\{f(x) \in C[0,1]\mid f(0)=0\}$. Is $\overline{M}=L^2[0,1]$?

score 57 · Answer 1 · 2015-03-10 02:36:10

57

Views

Let $M=\{f(x) \in C[0,1]\mid f(0)=0\}$. Is $\overline{M}=L^2[0,1]$?

Published on 10 Mar 2015 - 2:36

score 153 · Answer 2 · 2026-04-09 02:36:19

153

Views

$\|u\|_{L^{3}(\mathbb R)} \leq C \|Du\|_{L^{2}(\mathbb R)}^{\alpha} \|u\|_{L^{2}(\mathbb R)}^{1-\alpha}$?

Published on 09 Apr 2026 - 2:36

score 72 · Answer 3 · 2026-04-13 12:28:03

72

Views

Linear functionals over a non dense subset in $\ell^2$

Published on 13 Apr 2026 - 12:28

score 34 · Answer 4 · 2026-04-13 09:01:08

34

Views

If $u_n \to u$ in $L^2(\Omega)$, and $u_n \in L^\infty(\Omega)$, is $u \in L^\infty(\Omega)$?

Published on 13 Apr 2026 - 9:01

score 125 · Answer 5 · 2026-04-10 23:23:27

125

Views

Lebesgue's differentiation theorem for all points

Published on 10 Apr 2026 - 23:23

score 231 · Answer 6 · 2026-03-25 17:40:34

231

Views

Condition on $f$ in $L^{p, \infty} $ implies $f \in L^q$

Published on 25 Mar 2026 - 17:40

score 2.8k · Answer 7 · 2026-04-13 06:26:44

2.8k

Views

Prove that $\{\sin x, \sin 2x, ... , \sin nx\}$ is a linearly independent set

Published on 13 Apr 2026 - 6:26

score 91 · Answer 8 · 2015-03-17 13:41:24

91

Views

Does $f _n \to f $ pointwise imply $f _n $ converges to $f $ in $L ^p $ norm if $\{f_n\}$ is Cauchy in $L^p$?

Published on 17 Mar 2015 - 13:41

score 44 · Answer 9 · 2015-03-17 17:20:44

44

Views

Prove one limit

Published on 17 Mar 2015 - 17:20

score 56 · Answer 10 · 2026-04-10 14:11:22

56

Views

Dual of $L^\infty(I,H^1(M))$

Published on 10 Apr 2026 - 14:11

score 199 · Answer 11 · 2026-04-13 04:17:17

199

Views

Proving inequality that bounds the sum of norms with the norms of sums (plus additional terms)

Published on 13 Apr 2026 - 4:17

score 49 · Answer 12 · 2026-04-11 11:50:44

49

Views

Domain of a linear operator and using Interpolation Theorems

Published on 11 Apr 2026 - 11:50

score 601 · Answer 13 · 2015-03-20 16:33:11

601

Views

is $L^2 (\mathbb R)\subset L^\infty(\mathbb R)$?

Published on 20 Mar 2015 - 16:33

score 1.5k · Answer 14 · 2015-03-23 23:45:55

1.5k

Views

Convergence in $L^1_{loc}$ implies convergence almost everywhere

Published on 23 Mar 2015 - 23:45

score 54 · Answer 15 · 2015-03-24 05:19:45

54

Views

$\int_{\mathbb R}|f(x)|^{2} dx <\infty \implies \sum_{m\in \mathbb Z}\int_{m-\beta}^{m+\beta}|f(x)|^{2} dx <\infty$?

Published on 24 Mar 2015 - 5:19

List Question

Let $M=\{f(x) \in C[0,1]\mid f(0)=0\}$. Is $\overline{M}=L^2[0,1]$?

$\|u\|_{L^{3}(\mathbb R)} \leq C \|Du\|_{L^{2}(\mathbb R)}^{\alpha} \|u\|_{L^{2}(\mathbb R)}^{1-\alpha}$?

Linear functionals over a non dense subset in $\ell^2$

If $u_n \to u$ in $L^2(\Omega)$, and $u_n \in L^\infty(\Omega)$, is $u \in L^\infty(\Omega)$?

Lebesgue's differentiation theorem for all points

Condition on $f$ in $L^{p, \infty} $ implies $f \in L^q$

Prove that $\{\sin x, \sin 2x, ... , \sin nx\}$ is a linearly independent set

Does $f _n \to f $ pointwise imply $f _n $ converges to $f $ in $L ^p $ norm if $\{f_n\}$ is Cauchy in $L^p$?

Prove one limit

Dual of $L^\infty(I,H^1(M))$

Proving inequality that bounds the sum of norms with the norms of sums (plus additional terms)

Domain of a linear operator and using Interpolation Theorems

is $L^2 (\mathbb R)\subset L^\infty(\mathbb R)$?

Convergence in $L^1_{loc}$ implies convergence almost everywhere

$\int_{\mathbb R}|f(x)|^{2} dx <\infty \implies \sum_{m\in \mathbb Z}\int_{m-\beta}^{m+\beta}|f(x)|^{2} dx <\infty$?

Trending Questions

Popular # Hahtags

Popular Questions