Let $f: \mathbb{D} \backslash \{0, 1/2, 1/3, \dots \}$be an analytic bounded function. Can $f$ be necessarily extended to an analytic function on $\mathbb{D}?$
2026-05-15 10:21:29.1778840489
Extension of bounded analytic functions from a countable subset to the whole unit disk
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Yes. First note that it has a removable singularity at the points $\frac 1 2, \frac 1 3,...$. So we get an extension to $\mathbb D \setminus \{0\}$. Then extend to the whole of $\mathbb D$.