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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 \((\mu _{0},\mu _{1})\) 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 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
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