Characters and duality of locally compact Abelian groups

  • Edwin Hewitt
  • Kenneth A. Ross
Part of the Die Grundlehren der Mathematischen Wissenschaften book series (GMW)


This chapter is devoted to what might be called the “fine structure” of locally compact Abelian groups. We will obtain extremely detailed information about the structure of these groups. The basic tool in this program is the character group, which is defined and studied in §23. The character group is important in large measure because of the Pontryagin-van Kampen duality theorem, which is stated, proved, and utilized in §24. In §25, we apply the duality theorem to study a number of special locally compact Abelian groups, and in §26 we apply it to certain problems in structure theory and analysis.


Abelian Group Duality Theorem Continuous Character Character Group Cardinal Number 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1963

Authors and Affiliations

  • Edwin Hewitt
    • 1
  • Kenneth A. Ross
    • 2
  1. 1.The University of WashingtonUSA
  2. 2.The University of RochesterUSA

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