Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
function space
|
| gptkbp:alsoKnownAs |
space of square-integrable functions
|
| gptkbp:basisFor |
orthonormal basis exists
|
| gptkbp:complete |
true
|
| gptkbp:contains |
equivalence classes of functions
|
| gptkbp:containsElement |
measurable functions
|
| gptkbp:definedIn |
measure space
|
| gptkbp:functionsIdentifiedIf |
equal almost everywhere
|
| gptkbp:generalizes |
gptkb:Euclidean_space
|
| gptkbp:hasDual |
itself (self-dual)
|
| gptkbp:hasSubgroup |
Lp-space
|
| https://www.w3.org/2000/01/rdf-schema#label |
L^2-space
|
| gptkbp:importantFor |
gptkb:signal_processing
functional analysis quantum mechanics |
| gptkbp:innerProduct |
∫f(x)g(x) dμ(x)
|
| gptkbp:isHilbertSpace |
true
|
| gptkbp:L^2-norm |
(∫|f|^2 dμ)^{1/2}
|
| gptkbp:normDefinedBy |
gptkb:L^2-norm
|
| gptkbp:notation |
gptkb:L^2(X,_μ)
L^2(ℝ) |
| gptkbp:bfsParent |
gptkb:L^2(X,_μ)
|
| gptkbp:bfsLayer |
7
|