Question

How to get $[(-\Delta+\lambda)^{-1}u](x)=\int_{\mathbb{R}^3}\frac{\exp(-\sqrt{\lambda}\vert x-y \vert )}{4\pi \vert x-y \vert}u(y)dy$

score 156 · Answer 1 · 2018-06-10 11:08:11

156

Views

How to get $[(-\Delta+\lambda)^{-1}u](x)=\int_{\mathbb{R}^3}\frac{\exp(-\sqrt{\lambda}\vert x-y \vert )}{4\pi \vert x-y \vert}u(y)dy$

Published on 10 Jun 2018 - 11:08

score 144 · Answer 2 · 2026-03-25 11:22:44

144

Views

Show if pAp is a factor given a minimal projection

Published on 25 Mar 2026 - 11:22

score 123 · Answer 3 · 2026-03-25 20:35:36

123

Views

Theorem to rule out real (or imaginary) spectrum

Published on 25 Mar 2026 - 20:35

score 117 · Answer 4 · 2026-03-25 19:05:54

117

Views

Absolutely Continuous Spectrum of an operator $Af(x)=\sin x f(x)$

Published on 25 Mar 2026 - 19:05

score 46 · Answer 5 · 2018-06-11 08:55:46

46

Views

How about the Fourier transformation of $G(\theta,t)=1+2\sum_{n=1}^{\infty}e^{-n^2t}\cos n\theta$?

Published on 11 Jun 2018 - 8:55

score 51 · Answer 6 · 2026-03-25 11:18:45

51

Views

decomposition of a $C^*$ algebra

Published on 25 Mar 2026 - 11:18

score 54 · Answer 7 · 2026-03-26 18:49:57

54

Views

Classifying evolution operators with always-positive outputs given positive initial conditions

Published on 26 Mar 2026 - 18:49

score 37 · Answer 8 · 2018-06-11 18:41:56

37

Views

How can I get an expression for the operator norm?

Published on 11 Jun 2018 - 18:41

score 140 · Answer 9 · 2026-03-25 22:06:37

140

Views

Find the operator norm: $T\in B(L^{2}(\mathbb{R},e^{-x^{2}}dx)) $, $Tf(x) = f(x+1)$. $||T|| = $?

Published on 25 Mar 2026 - 22:06

score 178 · Answer 10 · 2026-03-25 11:18:09

178

Views

unitisation of $C^*\!$-algebra $A$

Published on 25 Mar 2026 - 11:18

score 59 · Answer 11 · 2026-03-25 11:23:37

59

Views

Decomposition of a finite dimensional representation of $C^*$ algebra

Published on 25 Mar 2026 - 11:23

score 57 · Answer 12 · 2018-06-12 13:56:36

57

Views

How to show $\ker (\lambda_{0}I-A)=E(D)\mathscr{H}, \forall \lambda_{0}\in \sigma_{d}(A)?$

Published on 12 Jun 2018 - 13:56

score 77 · Answer 13 · 2018-06-13 07:43:14

77

Views

How to prove $E(D)=\frac{1}{2\pi i}\oint_{\Gamma} (zI-A)^{-1}dz?$ where $A$ is self-adjoint.

Published on 13 Jun 2018 - 7:43

score 1.2k · Answer 14 · 2026-03-25 09:53:32

1.2k

Views

Eigenvectors of discrete Laplace matrix for 2D unit square under Neumann boundary condition

Published on 25 Mar 2026 - 9:53

score 1.3k · Answer 15 · 2026-03-26 01:02:38

1.3k

Views

Trace cauchy schwarz inequality

Published on 26 Mar 2026 - 1:02

List Question

How to get $[(-\Delta+\lambda)^{-1}u](x)=\int_{\mathbb{R}^3}\frac{\exp(-\sqrt{\lambda}\vert x-y \vert )}{4\pi \vert x-y \vert}u(y)dy$

Show if pAp is a factor given a minimal projection

Theorem to rule out real (or imaginary) spectrum

Absolutely Continuous Spectrum of an operator $Af(x)=\sin x f(x)$

How about the Fourier transformation of $G(\theta,t)=1+2\sum_{n=1}^{\infty}e^{-n^2t}\cos n\theta$?

decomposition of a $C^*$ algebra

Classifying evolution operators with always-positive outputs given positive initial conditions

How can I get an expression for the operator norm?

Find the operator norm: $T\in B(L^{2}(\mathbb{R},e^{-x^{2}}dx)) $, $Tf(x) = f(x+1)$. $||T|| = $?

unitisation of $C^*\!$-algebra $A$

Decomposition of a finite dimensional representation of $C^*$ algebra

How to show $\ker (\lambda_{0}I-A)=E(D)\mathscr{H}, \forall \lambda_{0}\in \sigma_{d}(A)?$

How to prove $E(D)=\frac{1}{2\pi i}\oint_{\Gamma} (zI-A)^{-1}dz?$ where $A$ is self-adjoint.

Eigenvectors of discrete Laplace matrix for 2D unit square under Neumann boundary condition

Trace cauchy schwarz inequality

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