Statements (19)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
compact domains
continuous symmetric positive semi-definite kernels |
| gptkbp:describes |
conditions for representing positive definite kernels as sums of eigenfunctions
|
| gptkbp:field |
gptkb:mathematics
functional analysis integral equations |
| https://www.w3.org/2000/01/rdf-schema#label |
Mercer's theorem
|
| gptkbp:namedAfter |
gptkb:James_Mercer
|
| gptkbp:publicationYear |
1909
|
| gptkbp:publishedIn |
gptkb:Proceedings_of_the_London_Mathematical_Society
|
| gptkbp:relatedTo |
gptkb:Hilbert-Schmidt_operators
spectral theory eigenfunction expansion |
| gptkbp:sentence |
If K(x, y) is a continuous symmetric positive semi-definite kernel on a compact domain, then it can be represented as a sum of eigenfunctions with non-negative eigenvalues.
|
| gptkbp:usedIn |
gptkb:machine_learning
support vector machines |
| gptkbp:bfsParent |
gptkb:kernel_methods
|
| gptkbp:bfsLayer |
5
|