The Peter-Weyl Theorem
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.
KeywordsMatrix Coefficient Compact Group Unitary Representation Irreducible Unitary Representation Matrix Group
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