Topological groups, Lie groups Locally compact abelian groups and Pontryagin duality Concept
Locally compact abelian group
Summary
A locally compact abelian group, or LCA group, is a commutative topological group whose topology is Hausdorff and locally compact. These groups are the natural setting of Fourier analysis. Each LCA group has a Haar measure and a dual group of characters, and Pontryagin duality says that the group is recovered from its dual.
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About this page
| Tag | ZR09S9R3AW |
|---|---|
| URI | m2://ZR09S9R3AW |
| Kind | concept |
| Writing | W0 stub |
| MSC | 22B05, 43A40 |
| Specializes | Locally compact group |
| Same as |
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Used by
- Harmonic analysis on groups
- Fourier transform on locally compact abelian groups
- Pontryagin dual
- Structure theorem for compactly generated LCA groups
- Pontryagin duality theorem
- Wiener's Tauberian theorem
- Plancherel theorem for abelian groups
- Bochner's theorem