Statements (28)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
function space |
| gptkbp:alsoKnownAs |
gptkb:Hilbert_space
gptkb:Lebesgue_space_L2 |
| gptkbp:basisFor |
orthonormal basis exists
|
| gptkbp:consistsOf |
square-integrable functions
|
| gptkbp:contains |
continuous functions with compact support
step functions zero function |
| gptkbp:definedIn |
measure space
|
| gptkbp:dimensions |
infinite (for infinite measure space)
|
| gptkbp:hasDual |
itself (self-dual)
|
| gptkbp:hasSubgroup |
gptkb:Lp_space
|
| https://www.w3.org/2000/01/rdf-schema#label |
L2 space
|
| gptkbp:innerProductDefinedBy |
integral of product of functions
|
| gptkbp:innerProductFormula |
∫f(x)g(x)dμ(x)
|
| gptkbp:isBanachSpace |
true
|
| gptkbp:isHilbertSpace |
true
|
| gptkbp:normDefinedBy |
L2 norm
|
| gptkbp:normFormula |
(∫|f|^2 dμ)^{1/2}
|
| gptkbp:numberOfIssues |
true
|
| gptkbp:symbol |
L^2
|
| gptkbp:usedIn |
gptkb:probability_theory
gptkb:signal_processing functional analysis quantum mechanics |
| gptkbp:bfsParent |
gptkb:Hilbert_space
|
| gptkbp:bfsLayer |
4
|