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Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
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Does a bounded real function have an analytic continuation [closed]
Consider the function $f:[0,1]\rightarrow\mathbb{R}$, where
$f$ is real-analytic on the open interval $(0,1)$
$f$ is bounded on the closed interval $[0,1]$ (ie. there is some constant $C$ such that …