On optimal algorithms for problems defined on groups (Q1824380)

The author considers an interpolation problem and a uniform approximation problem for certain mappings from the one-dimensional sphere \(S^ 1\) into itself. With the help of the universal covering map \({\mathbb{R}}\ni x\mapsto \exp (2\pi ix)\in S^ 1\) the above problems are reduced to ones for the corresponding functions from [0,1]\(\to {\mathbb{R}}\). Finally, optimality-preserving problem transformations are derived.