Abstract
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.
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© 2002 Springer Science+Business Media New York
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Deitmar, A. (2002). The Peter-Weyl Theorem. In: A First Course in Harmonic Analysis. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3834-6_10
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DOI: https://doi.org/10.1007/978-1-4757-3834-6_10
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-3836-0
Online ISBN: 978-1-4757-3834-6
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