  We define and study entanglement of continuous positive definite functions on
products of compact groups. We formulate and prove an infinite-dimensional
analog of Horodecki Theorem, giving a necessary and sufficient criterion for
separability of such functions. The resulting characterisation is given in
terms of mappings of the space of continuous functions, preserving positive
definiteness. The relation between the developed group-theoretical formalism
and the conventional one, given in terms of density matrices, is established
through the non-commutative Fourier analysis.
