Pontryagin duality

In mathematics, in particular in harmonic analysis and the theory of topological groups, Pontryagin duality explains the general properties of the Fourier transform. It places in a unified context a number of observations about functions on the real line or on finite abelian groups:

History

The foundations for the theory of locally compact abelian groups and their duality was laid down by Lev Semenovich Pontryagin in 1934. His 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 E.R. van Kampen in 1935 and André Weil in 1953.

Related Topics:
Lev Semenovich Pontryagin - Second-countable - E.R. van Kampen - André Weil

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