Question

Weyl's asymptotic law for eigenvalues - Rectangle $D = \{0 < x < a, 0 < y < b \}$

score 185 · Answer 1 · 2016-06-02 15:59:59

185

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Weyl's asymptotic law for eigenvalues - Rectangle $D = \{0 < x < a, 0 < y < b \}$

Published on 02 Jun 2016 - 15:59

score 326 · Answer 2 · 2016-06-04 03:06:13

326

Views

Weyl's asymptotic law for eigenvalue on the rectangle $D = \{0 < x < a, 0 < y < b \}$ - $N(\lambda) \geq \frac{\lambda ab}{4 \pi} - C \sqrt{\lambda}$

Published on 04 Jun 2016 - 3:06

score 239 · Answer 3 · 2016-06-05 21:39:41

239

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The bigger the domain, the smaller the first eigenvalue - $\lambda(M_2) \leq \lambda(M_1)$ on the Laplacian

Published on 05 Jun 2016 - 21:39

score 36 · Answer 4 · 2016-06-06 01:59:50

36

Views

If we know Spec($M_1$) and Spec($M_2$), what could we say about Spec($M_1 \cup M_2$)?

Published on 06 Jun 2016 - 1:59

score 329 · Answer 5 · 2016-06-14 09:41:32

329

Views

variational principle for the principal eigenvalue

Published on 14 Jun 2016 - 9:41

score 742 · Answer 6 · 2016-06-17 02:38:25

742

Views

Solving $\sin(\sqrt{\lambda}L) + \beta \cos(\sqrt{\lambda}L)\sqrt{\lambda} = 0$

Published on 17 Jun 2016 - 2:38

score 48 · Answer 7 · 2016-06-18 19:26:01

48

Views

Can "eigenvalues" in eigenfunction expansion be non-scalar?

Published on 18 Jun 2016 - 19:26

score 4.7k · Answer 8 · 2016-06-22 08:09:45

4.7k

Views

Boundary value problems: eigenvalue and eigenfunction

Published on 22 Jun 2016 - 8:09

score 288 · Answer 9 · 2016-06-23 01:46:53

288

Views

Spherical Harmonics & Beltrami operator

Published on 23 Jun 2016 - 1:46

score 35 · Answer 10 · 2016-06-25 18:07:04

35

Views

Eigenfunctions of $x^2M''+xM'+\lambda M=0$ with $M'(1)=0$ and $M'(L)=0$

Published on 25 Jun 2016 - 18:07

score 75 · Answer 11 · 2016-06-25 19:24:32

75

Views

Showing that ODE is not of Sturm-Liouville form

Published on 25 Jun 2016 - 19:24

score 49 · Answer 12 · 2016-06-26 02:12:02

49

Views

Solution to the boundary value problem $y''+\left(\frac{(1-e^{-4x})^2}{2x^3}-\frac{2(1-e^{-4x})}{x}\right)y'-\frac{(1-e^{-4x})^4}{16x^4} y=0$

Published on 26 Jun 2016 - 2:12

score 51 · Answer 13 · 2016-06-29 17:18:00

51

Views

If $\,\Delta_{\scriptsize\mathbb{R}^n}u = \lambda u\,$ and $\,u(x)=u(x+y)$, then $\,u_{y}(x):=e^{2 \pi i \left\langle x,y\right\rangle}$

Published on 29 Jun 2016 - 17:18

score 129 · Answer 14 · 2016-07-02 21:38:53

129

Views

Eigensolver for Black-box matrix

Published on 02 Jul 2016 - 21:38

score 193 · Answer 15 · 2016-07-04 01:14:54

193

Views

How could I find an orthogonal basis for $H^k$? - HELP!!

Published on 04 Jul 2016 - 1:14

List Question

Weyl's asymptotic law for eigenvalues - Rectangle $D = \{0 < x < a, 0 < y < b \}$

Weyl's asymptotic law for eigenvalue on the rectangle $D = \{0 < x < a, 0 < y < b \}$ - $N(\lambda) \geq \frac{\lambda ab}{4 \pi} - C \sqrt{\lambda}$

The bigger the domain, the smaller the first eigenvalue - $\lambda(M_2) \leq \lambda(M_1)$ on the Laplacian

If we know Spec($M_1$) and Spec($M_2$), what could we say about Spec($M_1 \cup M_2$)?

variational principle for the principal eigenvalue

Solving $\sin(\sqrt{\lambda}L) + \beta \cos(\sqrt{\lambda}L)\sqrt{\lambda} = 0$

Can "eigenvalues" in eigenfunction expansion be non-scalar?

Boundary value problems: eigenvalue and eigenfunction

Spherical Harmonics & Beltrami operator

Eigenfunctions of $x^2M''+xM'+\lambda M=0$ with $M'(1)=0$ and $M'(L)=0$

Showing that ODE is not of Sturm-Liouville form

Solution to the boundary value problem $y''+\left(\frac{(1-e^{-4x})^2}{2x^3}-\frac{2(1-e^{-4x})}{x}\right)y'-\frac{(1-e^{-4x})^4}{16x^4} y=0$

If $\,\Delta_{\scriptsize\mathbb{R}^n}u = \lambda u\,$ and $\,u(x)=u(x+y)$, then $\,u_{y}(x):=e^{2 \pi i \left\langle x,y\right\rangle}$

Eigensolver for Black-box matrix

How could I find an orthogonal basis for $H^k$? - HELP!!

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