Pontryagin's duality theorem
GPTKB entity
Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
locally compact abelian groups
|
| gptkbp:field |
gptkb:mathematics
gptkb:topology harmonic analysis |
| https://www.w3.org/2000/01/rdf-schema#label |
Pontryagin's duality theorem
|
| gptkbp:implies |
the dual of the dual group is canonically isomorphic to the original group
|
| gptkbp:namedAfter |
gptkb:Lev_Pontryagin
|
| gptkbp:publishedIn |
gptkb:Mathematische_Annalen
|
| gptkbp:relatedTo |
gptkb:Fourier_transform
gptkb:Pontryagin_duality |
| gptkbp:state |
The category of locally compact abelian groups is self-dual via the Pontryagin duality functor.
|
| gptkbp:usedIn |
Fourier analysis
representation theory abstract harmonic analysis |
| gptkbp:yearProposed |
1934
|
| gptkbp:bfsParent |
gptkb:Soviet_school_of_topology
|
| gptkbp:bfsLayer |
8
|