Question

Is it true that $\|f_n \ast g_n\|_{L^r(\mathbb{R}^{n})} \to \|f \ast g\|_{L^r(\mathbb{R}^{n})}$ as $n \to \infty$? (Young's inequality)

score 218 · Answer 1 · 2020-09-01 15:08:43

218

Views

Is it true that $\|f_n \ast g_n\|_{L^r(\mathbb{R}^{n})} \to \|f \ast g\|_{L^r(\mathbb{R}^{n})}$ as $n \to \infty$? (Young's inequality)

Published on 01 Sep 2020 - 15:08

score 244 · Answer 2 · 2020-09-03 02:38:42

244

Views

If $f$ is strictly convex and $f(x) = \infty$, is $x$ a boundary point?

Published on 03 Sep 2020 - 2:38

score 41 · Answer 3 · 2020-09-04 03:39:27

41

Views

Closeness of complemented subspace in TVS

Published on 04 Sep 2020 - 3:39

score 37 · Answer 4 · 2020-09-10 00:59:37

37

Views

Is it possible for a right triangle (drawn on some specific topology) to have all sides with equal lenth?

Published on 10 Sep 2020 - 0:59

score 266 · Answer 5 · 2026-03-25 23:37:13

266

Views

Is the strong topology on $B(H)$ first countable?

Published on 25 Mar 2026 - 23:37

score 58 · Answer 6 · 2020-09-12 08:09:21

58

Views

Show that the intersection of two sets is empty

Published on 12 Sep 2020 - 8:09

score 196 · Answer 7 · 2020-09-13 20:56:08

196

Views

How to fix this argument that the periodic functions on $[-L/2,L/2]$ generate a dense subspace of $L^2[-L/2,L/2]$?

Published on 13 Sep 2020 - 20:56

score 570 · Answer 8 · 2020-09-14 04:30:47

570

Views

Take a continuous map from a product topology, and fix one of the 2 arguments. Is the resultant map continuous?

Published on 14 Sep 2020 - 4:30

score 224 · Answer 9 · 2020-09-16 23:18:16

224

Views

Discontinuous functionals on infinite dimensional topological vector space

Published on 16 Sep 2020 - 23:18

score 251 · Answer 10 · 2020-09-17 08:14:36

251

Views

If $S$ is convex then $\text{cl}\big(\text{int}(S)\big)=\text{cl}(S)$ when $\text{int}(S)\neq\emptyset$

Published on 17 Sep 2020 - 8:14

score 515 · Answer 11 · 2020-09-17 09:10:10

515

Views

If $S$ is convex then $\text{cl}(S)$ and $\text{int}(S)$ are convex too.

Published on 17 Sep 2020 - 9:10

score 168 · Answer 12 · 2020-09-18 09:20:16

168

Views

Prove that if $a\in\text{int}(S)$ and $b\in\text{cl}(S)$ then $[a,b)\subseteq\text{int}(S)$ when $S$ is convex.

Published on 18 Sep 2020 - 9:20

score 197 · Answer 13 · 2026-03-27 03:57:44

197

Views

If a convex set affinely generates $\mathbb{R}^{n}$, does it have nonempty interior?

Published on 27 Mar 2026 - 3:57

score 126 · Answer 14 · 2026-02-23 19:19:46

126

Views

For normed linear spaces, uniform boundedness is equivalent to equicontinuity

Published on 23 Feb 2026 - 19:19

score 256 · Answer 15 · 2026-03-27 17:50:27

256

Views

Does a strictly convex and continuous function always exist?

Published on 27 Mar 2026 - 17:50

List Question

Is it true that $\|f_n \ast g_n\|_{L^r(\mathbb{R}^{n})} \to \|f \ast g\|_{L^r(\mathbb{R}^{n})}$ as $n \to \infty$? (Young's inequality)

If $f$ is strictly convex and $f(x) = \infty$, is $x$ a boundary point?

Closeness of complemented subspace in TVS

Is it possible for a right triangle (drawn on some specific topology) to have all sides with equal lenth?

Is the strong topology on $B(H)$ first countable?

Show that the intersection of two sets is empty

How to fix this argument that the periodic functions on $[-L/2,L/2]$ generate a dense subspace of $L^2[-L/2,L/2]$?

Take a continuous map from a product topology, and fix one of the 2 arguments. Is the resultant map continuous?

Discontinuous functionals on infinite dimensional topological vector space

If $S$ is convex then $\text{cl}\big(\text{int}(S)\big)=\text{cl}(S)$ when $\text{int}(S)\neq\emptyset$

If $S$ is convex then $\text{cl}(S)$ and $\text{int}(S)$ are convex too.

Prove that if $a\in\text{int}(S)$ and $b\in\text{cl}(S)$ then $[a,b)\subseteq\text{int}(S)$ when $S$ is convex.

If a convex set affinely generates $\mathbb{R}^{n}$, does it have nonempty interior?

For normed linear spaces, uniform boundedness is equivalent to equicontinuity

Does a strictly convex and continuous function always exist?

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