Convolutions and group representations

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


In the present chapter, we initiate our study of harmonic analysis proper. The basic operation in harmonic analysis is convolution; in §19, we give a reasonably general definition of convolutions and develop with some care the fundamental properties of convolutions of measures. In §20, we examine explicit formulas for convolutions of measures and functions. In §21, we present some facts about representations of groups and algebras. In §22, we prove the existence of irreducible representations of locally compact groups.


Unitary Representation Haar Measure Representation Versus Compact Abelian Group Cyclic Vector 
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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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