Weyl's law for domains in Euclidean space
GPTKB entity
Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
bounded domains in Euclidean space
|
| gptkbp:describes |
asymptotic distribution of eigenvalues of the Laplacian
|
| gptkbp:field |
gptkb:spectral_geometry
mathematical analysis |
| gptkbp:firstPublished |
1911
|
| gptkbp:hasApplication |
mathematical physics
quantum mechanics geometry of manifolds |
| https://www.w3.org/2000/01/rdf-schema#label |
Weyl's law for domains in Euclidean space
|
| gptkbp:namedAfter |
gptkb:Hermann_Weyl
|
| gptkbp:relatedTo |
gptkb:Laplace_operator
spectral theory eigenvalue problem asymptotic analysis |
| gptkbp:sentence |
The number of Dirichlet eigenvalues less than or equal to λ grows asymptotically as C·λ^{n/2} for large λ, where C depends on the volume of the domain and the dimension n.
|
| gptkbp:bfsParent |
gptkb:Weyl's_law_for_manifolds
|
| gptkbp:bfsLayer |
8
|