Weyl's law for smooth domains
GPTKB entity
Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
bounded smooth domains in Euclidean space
|
| gptkbp:borders |
gptkb:Dirichlet
|
| gptkbp:describes |
asymptotic distribution of eigenvalues of the Laplace operator
|
| gptkbp:field |
gptkb:spectral_geometry
mathematical analysis |
| gptkbp:form |
N(λ) ~ (ω_n/(2π)^n)·Vol(Ω)·λ^{n/2} as λ→∞
|
| gptkbp:generalizes |
gptkb:Weyl's_law_for_manifolds
|
| https://www.w3.org/2000/01/rdf-schema#label |
Weyl's law for smooth domains
|
| gptkbp:Laplace_operator |
Δ
|
| gptkbp:N(λ) |
number of eigenvalues less than λ
|
| gptkbp:namedAfter |
gptkb:Hermann_Weyl
|
| gptkbp:relatedTo |
spectral theory
eigenvalue problem |
| gptkbp:sentence |
The number of Dirichlet eigenvalues less than λ grows asymptotically as C·λ^{n/2} for large λ, where C depends on the volume of the domain.
|
| gptkbp:usedIn |
mathematical physics
quantum mechanics |
| gptkbp:yearProposed |
1911
|
| gptkbp:Ω |
smooth bounded domain in R^n
|
| gptkbp:ω_n |
volume of the unit ball in R^n
|
| gptkbp:bfsParent |
gptkb:Weyl's_law_for_fractal_drums
|
| gptkbp:bfsLayer |
6
|