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Pontryagin duality — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Pontryagin_duality
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Pontryagin duality — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Pontryagin_duality (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_ec2fc4ee9183 (Metraipolis archive dc_ec2fc4ee9183, sha256 aafc15c43e57b6fa37dbd7ece3b150fdac6c4fa92fca756c2ff99b87a07ce3cd)

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@misc{dcec2fc4ee9183,
  title = {Pontryagin duality — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Pontryagin_duality},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_ec2fc4ee9183; sha256 aafc15c43e57b6fa37dbd7ece3b150fdac6c4fa92fca756c2ff99b87a07ce3cd},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Pontryagin_duality. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In mathematics, Pontryagin duality is a duality between locally compact abelian groups that allows generalizing Fourier transform to all such groups, which include the circle group (the multiplicative group of complex numbers of modulus one), the finite abelian groups (with the discrete topology), and the additive group of the integers (also with the discrete topology), the real numbers, and every finite-dimensional vector space over the reals or a p-adic field. The Pontryagin dual of a locally compact abelian group is the locally compact abelian topological group, consisting of the continuous group homomorphisms from the group to the circle group, with the operation of pointwise multiplication and the topology of uniform convergence on compact sets. The Pontryagin duality theorem establishes Pontryagin duality by stating that any locally compact abelian group is naturally isomorphic with its bidual (the dual of its dual). The Fourier inversion theorem is a special case of this theorem. The subject is named after Lev Pontryagin, who laid down the foundations for the theory of locally compact abelian groups and their duality during his early mathematical works in 1934. Pontryagin's treatment relied on the groups being second-countable and either compact or discrete. This was improved to cover the general locally compact abelian groups by Egbert van Kampen in 1935 and André Weil in 1940.

Tema degli esploratori: fisica e astronomia (deposito sistematico; ricerca «quantum computing»).
Fonte: Wikipedia in inglese, voce «Pontryagin duality» — https://en.wikipedia.org/wiki/Pontryagin_duality
Wikidata Q1632419 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q1632419
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Pontryagin_duality?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1372943796, consultata il 2026-10-07T16:20:00.430Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 99bbbb1bd1a9d864eb989559dd8a35c88ddd7a23640ee72acbb225cd34790e25