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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

5 votes
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Induced group action of the left regular representation strongly continuous

Let $G$ be a compact group and let $\lambda: G \rightarrow \mathcal{U}(L^2(G))$ be the left regular representation, i.e. $\lambda_sf(t)=f(s^{-1}t)$. Why is the induced group action $\overline{\lambda …
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