Let $T:S^1\to C^\ast$ be a group theoretic homomorphism from the circle to the non-zero complex numbers. Presumably it is true that if $T$ is $L^2$, then it is continuous. Is there a simple proof, or a pointer to the literature?

Asked

Viewed
79 times

Every measurable homomorphism from $\mathbb{R}^n$ to $\mathbb{C}^*$ is exponential. The $L^2$ assumption plays no role. $\endgroup$ – YCor Nov 6 at 13:01