I've been asked to diagonalise an operator on $L^2(\mathbb{T})$, given by $Tf(z) = f(z^{-1}$). I know that I'm expected to find a $U$ such that $TU = UM_f$, where $M_f$ is the multiplication operator, however I can't seem to construct the $U$ that does this. Could anyone provide any hints?
2026-03-30 07:12:36.1774854756
Diagonalizing operator over $L^2(\mathbb{T})$
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