Statements (29)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
function space
|
| gptkbp:alsoKnownAs |
gptkb:L2_space
space of square-integrable functions |
| gptkbp:basisFor |
orthonormal basis exists
|
| gptkbp:complete |
true
|
| gptkbp:consistsOf |
measurable functions
|
| gptkbp:definedIn |
measure space
|
| gptkbp:hasDual |
itself (self-dual)
|
| gptkbp:hasSubgroup |
gptkb:Lp_spaces
|
| gptkbp:heldBy |
gptkb:Hilbert_space
|
| https://www.w3.org/2000/01/rdf-schema#label |
Lebesgue space L2
|
| gptkbp:importantFor |
gptkb:probability_theory
gptkb:signal_processing functional analysis quantum mechanics |
| gptkbp:innerProduct |
∫f(x)g(x) dμ(x)
|
| gptkbp:namedAfter |
gptkb:Henri_Lebesgue
|
| gptkbp:norm |
L2 norm
|
| gptkbp:normFormula |
(∫|f|^2 dμ)^{1/2}
|
| gptkbp:notation |
gptkb:L^2(X,_μ)
L2(X) L2(μ) |
| gptkbp:property |
functions whose absolute value squared is Lebesgue integrable
|
| gptkbp:separates |
true
|
| gptkbp:usedFor |
gptkb:PDEs
Fourier analysis stochastic processes |
| gptkbp:bfsParent |
gptkb:L2_space
|
| gptkbp:bfsLayer |
5
|