Question

Is the inner product $\langle \cdot, \cdot\rangle$ lower semi-continuous w.r.t. the product of weak topologies?

score 94 · Answer 1 · 2026-04-13 23:22:34

94

Views

Is the inner product $\langle \cdot, \cdot\rangle$ lower semi-continuous w.r.t. the product of weak topologies?

Published on 13 Apr 2026 - 23:22

score 60 · Answer 2 · 2026-03-26 06:32:32

60

Views

Fix $f \in H$ and let $u_n$ be the projection of $f$ onto $K_n$. Prove that $(u_n)$ converges in $H$

Published on 26 Mar 2026 - 6:32

score 57 · Answer 3 · 2026-04-11 19:01:10

57

Views

Explicit Feature Maps of the Kernel Trick?

Published on 11 Apr 2026 - 19:01

score 83 · Answer 4 · 2026-04-13 00:12:28

83

Views

Heisenberg Inequality for $L^2$ functions

Published on 13 Apr 2026 - 0:12

score 26 · Answer 5 · 2023-04-29 07:57:21

26

Views

Let $u_n$ be the projection of $f$ on $K_n$ with $K_n \subset K_{n+1}$. Prove that $(u_n)$ converges

Published on 29 Apr 2023 - 7:57

score 25 · Answer 6 · 2026-04-11 18:34:43

25

Views

Showing that $f_v\left(\bigotimes_{k=1}^3e_k\right)=\left<e_3,v\right>e_1\otimes e_2$ is a unique continuous map

Published on 11 Apr 2026 - 18:34

score 75 · Answer 7 · 2026-04-11 05:23:48

75

Views

An example of dense subspace of $\ell_2$

Published on 11 Apr 2026 - 5:23

score 91 · Answer 8 · 2026-04-13 20:37:18

91

Views

Determine the orthogonal projection of $f$ onto $K := \{u \in H : |u| \le h \text{ a.e.}\}$

Published on 13 Apr 2026 - 20:37

score 55 · Answer 9 · 2026-04-13 13:09:26

55

Views

If $a,e_1,\dots,e_n\in H$ for a Hilbert space $H$, then $\|a\otimes\bigotimes_{i=1}^ne_i\|^2=|\|a\|^2\|\bigotimes_{i=1}^ne_i\|^2$

Published on 13 Apr 2026 - 13:09

score 94 · Answer 10 · 2026-04-11 05:13:56

94

Views

A confusion about Brezis' exercise 5.10

Published on 11 Apr 2026 - 5:13

score 43 · Answer 11 · 2023-05-02 06:35:36

43

Views

Prove that $F(u) \le F(v)$ for all $v \in K$ IFF $\langle \nabla F(u), v-u) \ge 0$ for all $v \in K$

Published on 02 May 2023 - 6:35

score 24 · Answer 12 · 2026-04-12 01:03:56

24

Views

Inclusion into even, resp. odd indices is homotopic to identity?

Published on 12 Apr 2026 - 1:03

score 19 · Answer 13 · 2026-03-25 12:54:47

19

Views

On showing that $T^*\text{ is unique on } H\implies\mathscr{D}(T)\text{ is dense in $H$}$

Published on 25 Mar 2026 - 12:54

score 125 · Answer 14 · 2023-05-02 17:09:32

125

Views

Proof that $L^2 (Ω, F, P)$ is a Hilbert space

Published on 02 May 2023 - 17:09

score 82 · Answer 15 · 2026-04-13 12:47:38

82

Views

Spectral projection at $\{0\}$

Published on 13 Apr 2026 - 12:47

List Question

Is the inner product $\langle \cdot, \cdot\rangle$ lower semi-continuous w.r.t. the product of weak topologies?

Fix $f \in H$ and let $u_n$ be the projection of $f$ onto $K_n$. Prove that $(u_n)$ converges in $H$

Explicit Feature Maps of the Kernel Trick?

Heisenberg Inequality for $L^2$ functions

Let $u_n$ be the projection of $f$ on $K_n$ with $K_n \subset K_{n+1}$. Prove that $(u_n)$ converges

Showing that $f_v\left(\bigotimes_{k=1}^3e_k\right)=\left<e_3,v\right>e_1\otimes e_2$ is a unique continuous map

An example of dense subspace of $\ell_2$

Determine the orthogonal projection of $f$ onto $K := \{u \in H : |u| \le h \text{ a.e.}\}$

If $a,e_1,\dots,e_n\in H$ for a Hilbert space $H$, then $\|a\otimes\bigotimes_{i=1}^ne_i\|^2=|\|a\|^2\|\bigotimes_{i=1}^ne_i\|^2$

A confusion about Brezis' exercise 5.10

Prove that $F(u) \le F(v)$ for all $v \in K$ IFF $\langle \nabla F(u), v-u) \ge 0$ for all $v \in K$

Inclusion into even, resp. odd indices is homotopic to identity?

On showing that $T^*\text{ is unique on } H\implies\mathscr{D}(T)\text{ is dense in $H$}$

Proof that $L^2 (Ω, F, P)$ is a Hilbert space

Spectral projection at $\{0\}$

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