Almost periodic function on a group

Summary

An almost periodic function on a group is a bounded continuous function whose translates form a relatively compact set for uniform convergence. John von Neumann introduced the notion for arbitrary groups, extending Bohr's almost periodic functions on the real line. These functions are exactly the uniform limits of linear combinations of coefficients of finite-dimensional unitary representations. They are the continuous functions on the Bohr compactification pulled back to the group.