Question

Showing that the map that takes $u_0$ to solution $u(t)$ is self-adjoint

score 67 · Answer 1 · 2026-04-12 03:36:23

67

Views

Showing that the map that takes $u_0$ to solution $u(t)$ is self-adjoint

Published on 12 Apr 2026 - 3:36

score 170 · Answer 2 · 2026-04-04 08:46:26

170

Views

The algebras of compact operators on $\ell_p$ as direct limits of matrix algebras

Published on 04 Apr 2026 - 8:46

score 79 · Answer 3 · 2026-04-10 05:53:03

79

Views

Density of $L^\infty(\Omega)h$ in $L^p(\Omega)$ where $h \in L^p(\Omega)$

Published on 10 Apr 2026 - 5:53

score 116 · Answer 4 · 2026-04-16 17:14:47

116

Views

Doesn't this $L^p$ norm estimate for all $p$ give me an $L^\infty$ bound?

Published on 16 Apr 2026 - 17:14

score 148 · Answer 5 · 2026-04-14 05:13:26

148

Views

The convergence rate of the derivative of a sequence of function

Published on 14 Apr 2026 - 5:13

score 166 · Answer 6 · 2026-04-13 09:01:28

166

Views

The convergence of re-scaled function with mollification

Published on 13 Apr 2026 - 9:01

score 165 · Answer 7 · 2026-04-17 05:19:43

165

Views

Convergence in $L_p$ with $\sigma$-finite measure

Published on 17 Apr 2026 - 5:19

score 157 · Answer 8 · 2026-04-15 18:55:15

$T\colon L^2[0,1] \to L^2[0,1]$ be a bounded linear map of Hilbert spaces such that if $f\in L^2[0,1]$ is continuous then so is $Tf$.

score 118 · Answer 9 · 2026-03-10 04:26:12

118

Views

Using wavelets to capture the $L^2$ norm of $f''$

Published on 10 Mar 2026 - 4:26

score 121 · Answer 10 · 2026-04-15 08:18:31

121

Views

If $\mathcal{F}$ is the Fourier transform, what can be said about $\mathcal{F}(L^1(\mathbb{R})) \cap L^1(\mathbb{R})$?

Published on 15 Apr 2026 - 8:18

score 207 · Answer 11 · 2026-04-17 00:35:30

207

Views

Exists $C = C(\epsilon, p)$ where $\|u\|_{L^\infty(0, 1)} \le \epsilon\|u'\|_{L^p(0, 1)} + C\|u\|_{L^1(0, 1)}$ for all $u \in W^{1, p}(0, 1)$?

Published on 17 Apr 2026 - 0:35

score 88 · Answer 12 · 2026-04-15 22:43:03

88

Views

Followup question, does $\|u\|_{L^\infty(0, 1)} \le \epsilon\|u'\|_{L^p(0, 1)} + C\|u\|_{L^1(0, 1)}$ still hold when $p = 1$?

Published on 15 Apr 2026 - 22:43

score 172 · Answer 13 · 2026-04-13 23:23:39

172

Views

Is the subspace of $L^2([0,1])$ of all "functions" vanishing on $[0,1/2]$ closed?

Published on 13 Apr 2026 - 23:23

score 300 · Answer 14 · 2026-04-15 21:05:13

300

Views

Inequalities involving Sobolev spaces.

Published on 15 Apr 2026 - 21:05

score 336 · Answer 15 · 2026-04-16 22:50:12

336

Views

Relation of convergence in $L^\infty$ and $L^p$

Published on 16 Apr 2026 - 22:50

List Question

Showing that the map that takes $u_0$ to solution $u(t)$ is self-adjoint

The algebras of compact operators on $\ell_p$ as direct limits of matrix algebras

Density of $L^\infty(\Omega)h$ in $L^p(\Omega)$ where $h \in L^p(\Omega)$

Doesn't this $L^p$ norm estimate for all $p$ give me an $L^\infty$ bound?

The convergence rate of the derivative of a sequence of function

The convergence of re-scaled function with mollification

Convergence in $L_p$ with $\sigma$-finite measure

$T\colon L^2[0,1] \to L^2[0,1]$ be a bounded linear map of Hilbert spaces such that if $f\in L^2[0,1]$ is continuous then so is $Tf$.

Using wavelets to capture the $L^2$ norm of $f''$

If $\mathcal{F}$ is the Fourier transform, what can be said about $\mathcal{F}(L^1(\mathbb{R})) \cap L^1(\mathbb{R})$?

Exists $C = C(\epsilon, p)$ where $\|u\|_{L^\infty(0, 1)} \le \epsilon\|u'\|_{L^p(0, 1)} + C\|u\|_{L^1(0, 1)}$ for all $u \in W^{1, p}(0, 1)$?

Followup question, does $\|u\|_{L^\infty(0, 1)} \le \epsilon\|u'\|_{L^p(0, 1)} + C\|u\|_{L^1(0, 1)}$ still hold when $p = 1$?

Is the subspace of $L^2([0,1])$ of all "functions" vanishing on $[0,1/2]$ closed?

Inequalities involving Sobolev spaces.

Relation of convergence in $L^\infty$ and $L^p$

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