Question

Factoring Variable in $L^2$

score 23 · Answer 1 · 2026-03-25 05:59:13

23

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Factoring Variable in $L^2$

Published on 25 Mar 2026 - 5:59

score 117 · Answer 2 · 2019-03-05 15:19:12

117

Views

Can I equip the space $H^{1/2}(\partial \Omega)$ with a $L^2( \partial \Omega)$ inner product?

Published on 05 Mar 2019 - 15:19

score 187 · Answer 3 · 2019-03-05 18:49:35

187

Views

No non-negative continuous function on $[a,b]$ such that $\int_a^b f(t)dt=1, \int_a^b tf(t)dt=c, \int_a^b t^2f(t)dt=c^2$ for $c\in\mathbb{R}$.

Published on 05 Mar 2019 - 18:49

score 28 · Answer 4 · 2026-03-25 06:09:50

28

Views

Can anyone prove this proposition? (Frame Functions)

Published on 25 Mar 2026 - 6:09

score 1.2k · Answer 5 · 2019-03-06 12:08:42

1.2k

Views

Does Pythagorean law holds in Hilbert space or plane?

Published on 06 Mar 2019 - 12:08

score 83 · Answer 6 · 2026-03-25 03:22:13

83

Views

If $(\pi_λ)_{λ\in\mathbb R}$ is a family of orthogonal projections, do $λ↦\left\|\pi_λx\right\|_H^2$ and $λ↦\pi_λx$ have the same variation?

Published on 25 Mar 2026 - 3:22

score 36 · Answer 7 · 2019-03-07 12:00:20

Given $X$ Hilbert space, $T\in X^*$, $y$ projection of $x_0$ on $Y=\text{Ker}T$, why does $x-\frac{T(x)}{T(x_0-y)}(x_0-y)\in \text{Ker}T$?

score 40 · Answer 8 · 2019-03-08 17:58:36

40

Views

Let $a, b$, be positives and $a \leq b$. For which $p$ the function $\frac{1} {x^a+x^b}$ is $L_p(0,+\infty)$?

Published on 08 Mar 2019 - 17:58

score 61 · Answer 9 · 2019-03-10 19:01:34

61

Views

Improper integral convergence for different powers of a fraction

Published on 10 Mar 2019 - 19:01

score 53 · Answer 10 · 2026-03-28 09:54:14

53

Views

Sufficient condition to show density of $\mathcal{E}$ in $\Lambda^2$(Hilbert space)

Published on 28 Mar 2026 - 9:54

score 260 · Answer 11 · 2019-03-12 11:16:57

260

Views

Why is a finite metric spaces is not always of negative type?

Published on 12 Mar 2019 - 11:16

score 795 · Answer 12 · 2026-03-25 12:54:26

795

Views

Examples of non-unitary isometries on finite dimensional Hilbert spaces?

Published on 25 Mar 2026 - 12:54

score 39 · Answer 13 · 2019-03-13 09:53:55

39

Views

Density of a subspace

Published on 13 Mar 2019 - 9:53

score 328 · Answer 14 · 2026-03-26 13:57:18

328

Views

Show that graph of operator with adjoint operator is closed

Published on 26 Mar 2026 - 13:57

score 104 · Answer 15 · 2026-03-26 11:02:09

104

Views

If $A \in \mathcal{L}(H)$ and $\langle A(u),u \rangle \geq \langle u, u \rangle$, then $A$ is invertible.

Published on 26 Mar 2026 - 11:02

List Question

Factoring Variable in $L^2$

Can I equip the space $H^{1/2}(\partial \Omega)$ with a $L^2( \partial \Omega)$ inner product?

No non-negative continuous function on $[a,b]$ such that $\int_a^b f(t)dt=1, \int_a^b tf(t)dt=c, \int_a^b t^2f(t)dt=c^2$ for $c\in\mathbb{R}$.

Can anyone prove this proposition? (Frame Functions)

Does Pythagorean law holds in Hilbert space or plane?

If $(\pi_λ)_{λ\in\mathbb R}$ is a family of orthogonal projections, do $λ↦\left\|\pi_λx\right\|_H^2$ and $λ↦\pi_λx$ have the same variation?

Given $X$ Hilbert space, $T\in X^*$, $y$ projection of $x_0$ on $Y=\text{Ker}T$, why does $x-\frac{T(x)}{T(x_0-y)}(x_0-y)\in \text{Ker}T$?

Let $a, b$, be positives and $a \leq b$. For which $p$ the function $\frac{1} {x^a+x^b}$ is $L_p(0,+\infty)$?

Improper integral convergence for different powers of a fraction

Sufficient condition to show density of $\mathcal{E}$ in $\Lambda^2$(Hilbert space)

Why is a finite metric spaces is not always of negative type?

Examples of non-unitary isometries on finite dimensional Hilbert spaces?

Density of a subspace

Show that graph of operator with adjoint operator is closed

If $A \in \mathcal{L}(H)$ and $\langle A(u),u \rangle \geq \langle u, u \rangle$, then $A$ is invertible.

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