# Answer to Question #23719 in Abstract Algebra for Hym@n B@ss

Question #23719

Let Fk(G) be the k-space of class functions on G, given the inner product

[μ, ν] = 1/|G| *(Sum over g) μ(g^−1)ν(g).

Show that, for any class function f ∈ Fk(G), there is a “Fourier expansion” f = (sum over i) [f,χi] χi.

[μ, ν] = 1/|G| *(Sum over g) μ(g^−1)ν(g).

Show that, for any class function f ∈ Fk(G), there is a “Fourier expansion” f = (sum over i) [f,χi] χi.

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