Let $G$ be a compact group and $T$ a maximal torus on $G$. Suppose $f$ is an analytic function defined on $T$. Is there an analytic function $F$ on $G$ whose restriction agrees with $f$ on $T$?
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asked Sep 4, 2016 at 13:53
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1 Answer
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This seems to be consequence of the paper
Cartan, Henri: Variétés analytiques réelles et variétés analytiques complexes. Bull. Soc. Math. France 85 1957 77–99
Cartan shows more generally (see sections 6 and 7), that a real analytic function on a real analytic submanifold of $\mathbb R^n$ can be extended to a real analytic function on all of $\mathbb R^n$.
answered Sep 4, 2016 at 15:52
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3$\begingroup$ By the way, this old paper by H. Cartan is available online here numdam.org/numdam-bin/fitem?id=BSMF_1957__85__77_0 $\endgroup$ Commented Sep 4, 2016 at 23:37
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$\begingroup$ The link is now numdam.org/item/BSMF_1957__85__77_0 $\endgroup$ Commented Jan 11, 2019 at 17:45