Statements (28)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
function space |
| gptkbp:alsoKnownAs |
space of rapidly decreasing functions
|
| gptkbp:basisFor |
tempered distributions
|
| gptkbp:category |
gptkb:Fréchet_space
topological vector space |
| gptkbp:closed |
gptkb:Fourier_transform
differentiation multiplication by polynomials |
| gptkbp:complete |
yes
|
| gptkbp:definedIn |
gptkb:Euclidean_space
|
| gptkbp:field |
gptkb:mathematics
functional analysis distribution theory |
| gptkbp:hasSubgroup |
smooth functions
|
| https://www.w3.org/2000/01/rdf-schema#label |
Schwartz space
|
| gptkbp:introducedIn |
20th century
|
| gptkbp:namedAfter |
gptkb:Laurent_Schwartz
|
| gptkbp:nuclearSpace |
yes
|
| gptkbp:property |
functions are infinitely differentiable
functions and all derivatives decrease faster than any polynomial increases |
| gptkbp:symbol |
S(R^n)
|
| gptkbp:topology |
locally convex topology
|
| gptkbp:usedIn |
Fourier analysis
theory of distributions |
| gptkbp:bfsParent |
gptkb:Gelfand–Shilov_function
gptkb:Gelfand–Shilov_spaces |
| gptkbp:bfsLayer |
5
|