Coherent pairs of linear functionals on the unit circle

In this paper we extend the concept of coherent pairs of measures from the real line to Jordan arcs and curves. We present a characterization of pairs of coherent measures on the unit circle: it is established that if (μ0,μ1) is a coherent pair of measures on the unit circle, then μ0 is a semi-classical measure. Moreover, we obtain that the linear functional associated with μ1 is a specific rational transformation of the linear functional corresponding to μ0. Some examples are given.