The Peter-Weyl Theorem

  • Anton Deitmar
Part of the Universitext book series (UTX)


The Peter-Weyl theorem generalizes the completeness of the Fourier series, and so it is Plancherel’s theorem for compact groups. It states that for a compact group K the matrix coefficients of the finite-dimensional irreducible unitary representations give an orthonormal basis of L 2 (K). We will prove it here only for matrix groups.


Matrix Coefficient Compact Group Unitary Representation Irreducible Unitary Representation Matrix Group 
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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Anton Deitmar
    • 1
  1. 1.Department of MathematicsUniversity of ExeterExeter, DevonUK

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