Abstract
The functional equation of translation surfaces as introduced by Sophus Lie will be solved under various assumptions stemming from analysis, algebra or geometry. Quadratic functions are, especially, of interest in this connection. Some general solutions will be presented. The functional equation of twofold translation surfaces will be studied in different situations. For further results in the context of Lie’s functional equation of translation type see our paper (Benz and Reich, in Aequat Math 68:127–159, 2004).
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