Source Wikipedia
Published: 2013-09
Total Pages: 90
Get eBook
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 43. Chapters: Adelic algebraic group, Almost periodic function, Amenable group, Bohr compactification, Cantor cube, Chabauty topology, Circle group, Compactly generated group, Compact group, Covering group, Free regular set, Fundamental domain, Haar measure, Hilbert-Smith conjecture, Homeomorphism group, Homogeneous space, Identity component, Kazhdan's property (T), Kronecker's theorem, Locally compact group, Locally profinite group, Loop group, Mautner's lemma, Maximal compact subgroup, Monothetic group, Noncommutative harmonic analysis, No small subgroup, One-parameter group, Peter-Weyl theorem, Pontryagin duality, Principal homogeneous space, Pro-p group, Properly discontinuous action, Prosolvable group, Restricted product, Schwartz-Bruhat function, Solenoid (mathematics), System of imprimitivity, Tannaka-Krein duality, Topological abelian group, Topological group, Topological semigroup, Totally disconnected group, Von Neumann conjecture. Excerpt: In mathematics, specifically in harmonic analysis and the theory of topological groups, Pontryagin duality explains the general properties of the Fourier transform on locally compact groups, such as R, the circle or finite cyclic groups. The Pontryagin duality theorem itself states that locally compact groups identify naturally with their bidual. The subject is named after Lev Semenovich 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 group 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 Andre Weil in 1940. Pontryagin duality places in a unified context a number of observations about functions on the real line or on finite...