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Coherent pairs of linear functionals on the unit circle. (English) Zbl 1149.42013
Summary: 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 $\left({\mu }_{0},{\mu }_{1}\right)$ is a coherent pair of measures on the unit circle, then ${\mu }_{0}$ is a semi-classical measure. Moreover, we obtain that the linear functional associated with ${\mu }_{1}$ is a specific rational transformation of the linear functional corresponding to ${\mu }_{0}$. Some examples are given.
MSC:
 42C05 General theory of orthogonal functions and polynomials