Interpolation and prediction problems for connected compact abelian groups

Extensions of the Nehari theorem and of the Sarason commutation theorem are given for compact abelian groups whose dual have a complete linear order compatible with the group structure. As a special case a version of the classical interpolation theorem due to Carathéodory — Féjer is obtained.For these groups an extension of the Helson — Szegö theorem and integral representations for positive definite generalized Toeplitz kernels are given.Partially supported by the CDCH of the Universidad Central de Venezuela, and by CONICIT grant G-97000668.