Question

Proof verification: Characterising the domain of a self-adjoint operator

score 110 · Answer 1 · 2026-03-26 01:16:03

110

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Proof verification: Characterising the domain of a self-adjoint operator

Published on 26 Mar 2026 - 1:16

score 38 · Answer 2 · 2026-03-31 19:13:05

38

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Repeated Matrix Approximations / Approximation of Smaller Rank

Published on 31 Mar 2026 - 19:13

score 30 · Answer 3 · 2023-04-15 04:13:24

30

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Build $f, g >0$ so that $|\nabla f (x) |^2 \le g^2(f(x))$, $\lim_{|x| \to 0} f(x) = 0$, and $\int_0^a \frac{1}{g(t)}dt = \infty$ all $a > 0$

Published on 15 Apr 2023 - 4:13

score 29 · Answer 4 · 2023-04-17 02:12:26

29

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Show $\| \langle x \rangle^{s} (-\partial^2_x)^{1/2} \langle x \rangle^{-s} \varphi \|_{L^2} \le C\| \varphi \|_{H^1}$ for $\varphi \in C_0^\infty$

Published on 17 Apr 2023 - 2:12

score 77 · Answer 5 · 2023-04-19 04:58:07

77

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How to choose such self-adjoint operators here.

Published on 19 Apr 2023 - 4:58

score 53 · Answer 6 · 2023-04-20 22:53:16

53

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Why is the subset of all vectors whose spectral measure is absolutely continuous with respect to Lebesgue a subspace?

Published on 20 Apr 2023 - 22:53

score 53 · Answer 7 · 2026-03-28 05:59:28

53

Views

Discrete spectrum under a finite rank perturbation

Published on 28 Mar 2026 - 5:59

score 50 · Answer 8 · 2026-03-26 01:07:22

50

Views

Spectral Methods for PDE with mixed derivative

Published on 26 Mar 2026 - 1:07

score 301 · Answer 9 · 2026-03-30 03:05:22

301

Views

Reference request to the theory and examples of the spectrum of the Laplace-Beltrami operator on different compact manifolds

Published on 30 Mar 2026 - 3:05

score 146 · Answer 10 · 2026-03-26 19:17:23

146

Views

Is the antiderivative of an $L^2$ function always well-defined?

Published on 26 Mar 2026 - 19:17

score 19 · Answer 11 · 2023-04-27 14:52:03

19

Views

Bounds on graph spectrum for nonempty and for connected graphs

Published on 27 Apr 2023 - 14:52

score 49 · Answer 12 · 2023-04-29 07:25:10

49

Views

Find the spectrum of $Ax(t)=tx(t)$ where $A:L^2[0,1]\rightarrow L^2[0,1]$.

Published on 29 Apr 2023 - 7:25

score 180 · Answer 13 · 2026-02-23 22:48:18

180

Views

Coercivity and spectral gap: understanding the equivalence

Published on 23 Feb 2026 - 22:48

score 47 · Answer 14 · 2026-03-25 21:49:27

47

Views

Eigenfunctions of high order fractional operator

Published on 25 Mar 2026 - 21:49

score 85 · Answer 15 · 2026-03-28 07:07:23

85

Views

Where is the mistake in computing $\sigma(T)$?

Published on 28 Mar 2026 - 7:07

List Question

Proof verification: Characterising the domain of a self-adjoint operator

Repeated Matrix Approximations / Approximation of Smaller Rank

Build $f, g >0$ so that $|\nabla f (x) |^2 \le g^2(f(x))$, $\lim_{|x| \to 0} f(x) = 0$, and $\int_0^a \frac{1}{g(t)}dt = \infty$ all $a > 0$

Show $\| \langle x \rangle^{s} (-\partial^2_x)^{1/2} \langle x \rangle^{-s} \varphi \|_{L^2} \le C\| \varphi \|_{H^1}$ for $\varphi \in C_0^\infty$

How to choose such self-adjoint operators here.

Why is the subset of all vectors whose spectral measure is absolutely continuous with respect to Lebesgue a subspace?

Discrete spectrum under a finite rank perturbation

Spectral Methods for PDE with mixed derivative

Reference request to the theory and examples of the spectrum of the Laplace-Beltrami operator on different compact manifolds

Is the antiderivative of an $L^2$ function always well-defined?

Bounds on graph spectrum for nonempty and for connected graphs

Find the spectrum of $Ax(t)=tx(t)$ where $A:L^2[0,1]\rightarrow L^2[0,1]$.

Coercivity and spectral gap: understanding the equivalence

Eigenfunctions of high order fractional operator

Where is the mistake in computing $\sigma(T)$?

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