Fourier transforms

  • Edwin Hewitt
  • Kenneth A. Ross
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 152)


This chapter presents basic facts about Fourier transforms on both locally compact Abelian and arbitrary compact groups, many of which are needed for the detailed analysis in Chapters Nine, Ten, and Eleven. The Fourier transform as defined in (23.9) is a complex-valued function on the character group of a locally compact Abelian group. For a compact non-Abelian group, the Fourier transform is an operator-valued function defined on the dual object (28.34). Parts of the theory can be described simultaneously for compact and for locally compact Abelian groups, and we will do this wherever possible.


Compact Subset Compact Group Banach Algebra Haar Measure Character Group 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1970

Authors and Affiliations

  • Edwin Hewitt
    • 1
  • Kenneth A. Ross
    • 2
  1. 1.Department of Mathematic GN-50University of WashingtonSeattleUSA
  2. 2.Department of MathematicsUniversity of OregonEugeneUSA

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