In mathematics, Pontryagin duality is a duality between locally compact abelian groups that allows generalizing Fourier transform to all such groups, which...
39 KB (5,806 words) - 03:42, 8 May 2024
Lev Pontryagin (redirect from Pontrjagin)
Pontryagin (Russian: Лев Семёнович Понтрягин, also written Pontriagin or Pontrjagin, first name sometimes anglicized as Leon) (3 September 1908 – 3 May 1988)...
12 KB (1,032 words) - 00:35, 30 April 2024
its representation on the space of L2 functions on the unitary dual. Pontrjagin duality and the Peter–Weyl theorem achieve this for abelian and compact...
55 KB (7,184 words) - 17:41, 8 July 2024
group G = Zqω (the countable direct sum) is discrete. Although the Pontrjagin dual Γ is also Zqω, the topology of Γ is compact. One can see that Γ is...
45 KB (6,916 words) - 19:55, 12 May 2024
abelian group K, equipped with a Haar measure. Such a group has a Pontrjagin dual K ^ {\displaystyle {\hat {K}}} , consisting of all continuous U ( 1...
33 KB (5,894 words) - 04:24, 6 October 2024
unique number such that the group T, equipped with its Haar measure, is Pontrjagin dual to the lattice of integral multiples of 2π. This is a version of the...
147 KB (17,481 words) - 05:04, 23 September 2024
Chow motives of abelian varieties. In string theory, T-duality (short for target space duality), which relates two quantum field theories or string theories...
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Akbarov 2009, p. 468. Akbarov 2003, p. 272. Smith, M.F. (1952). "The Pontrjagin duality theorem in linear spaces". Annals of Mathematics. 56 (2): 248–253...
5 KB (711 words) - 21:26, 7 March 2023
Thom space (redirect from Pontrjagin-Thom construction)
classic reference for differential topology, treating the link to Poincaré duality, Euler class of Sphere bundles, Thom classes and Thom isomorphism, and...
13 KB (1,978 words) - 18:32, 31 July 2024
{\displaystyle S^{1}} with the Lie group framing. The isomorphism here is via the Pontrjagin-Thom construction. Define μ ( x ) ∈ Z 2 {\displaystyle \mu (x)\in \mathbb...
19 KB (3,422 words) - 10:37, 10 February 2024