Factorization of Cosine Functions on Compact Connected Groups

Based on the structure theorem of compact connected groups, the following factorization theorem is obtained in this paper: if a compact connected group G has direct factors isomorphic to SU(2), then non-classical cosine functions on G exist and each of them factors through one of these direct factors; otherwise, all cosine functions on G are classical. On the other hand, all cosine functions on SU(2) are obtained using some techniques on functional equations. Our main tools are from the structure theory of semisimple Lie groups.