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.

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

DIKRANJAN, Dikran;
2011

Abstract

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.
File in questo prodotto:
File Dimensione Formato  
AnkaraReprint.pdf

non disponibili

Tipologia: Versione Editoriale (PDF)
Licenza: Non pubblico
Dimensione 505.67 kB
Formato Adobe PDF
505.67 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11390/870554
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 2
social impact