Duality for Abelian Groups

Part of the Universitext book series (UTX)

In this chapter we are mainly interested in the study of abelian locally compact groups A, their dual groups  together with various associated group algebras. Using the Gelfand-Naimark Theorem as a tool, we shall then give a proof of the Plancherel Theorem, which asserts that the Fourier transform extends to a unitary equivalence of the Hilbert spaces L2 (A) and L2 (Â). We also prove the Pontryagin Duality Theorem that gives a canonical isomorphism between A and its bidual \(\widehat{\hat{ A\,}}\).


ABELIAN Group Banach Algebra Haar Measure Short Exact Sequence Inversion Formula 
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© Springer Science+Business Media, LLC 2009

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