Local analytic solutions of a functional equation

Andrzej Smajdor, Wilhelmina Smajdor


All analytic solutions of the functional equation
in the annulus
P:=\{z\in \mathbb{C}: 1-\epsilon\le|z|\le1+\epsilon\}
and in the domain
D:=\{z=re^{i\theta}\in \mathbb{C}: 1-\epsilon\le r \le 1+\epsilon, \theta\in (-\delta,\delta)\},
are found.

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