An elementary approach to Haar integration and Pontryagin duality in locally compact abelian groups

作者：Dikranjan Dikran; Stoyanov Luchezar^*

来源：Topology and Its Applications, 2011, 158(15): 1942-1961.

DOI：10.1016/j.topol.2011.06.037

• Haar integral
• Pontryagin duality
• Peter-Weyl theorem
• Almost periodic function
• Bohr-von Neumann theorem
• Locally compact abelian group
• Folner theorem

We offer an elementary proof of Pontryagin duality theorem for compact and discrete abelian groups. To this end we make use of an elementary proof of Peter-Weyl theorem due to Prodanov that makes no recourse to Haar integral. As a long series of applications of this approach we obtain proofs of Bohr-von Neumann's theorem on almost periodic functions, Comfort-Ross' theorem on the description of the precompact topologies on abelian groups, and, last but not least, the existence of Haar integral in LCA groups.

• 出版日期2011-9-15