I have a simple question: if $f:[-1,1]\to\mathbb{R}$ is analytic, can it be infinitely oscillatory (by which I mean something like $\sin(1/x)$ ?
2026-03-29 05:11:41.1774761101
Analyticity of infinitely oscillatory functions
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No, if $U=f^{-1} (f(x))$ is the preimage of $f(x)$ then $x$ must be isolated in $U$.