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A similar result holds for compact groups (not necessarily abelian): the matrix coefficients of finite-dimensional [[unitary representation|unitary representations]] form an orthonormal basis in ''L''² by the [[Peter-Weyl theorem]], and an analog of the convolution theorem continues to hold, along with many other aspects of [[harmonic analysis]] that depend on the Fourier transform.

 

Let ''G'' be a topological group.

If μ and ν are finite [[Borel measure|Borel measures]] on a group ''G'', then their convolution μ∗ν is defined by