Coherent pairs of linear functionals on the unit circle

16 pages, no figures.-- 2000 MSC code: Primary 42C05.MR#: MR2432558 (2009e:42048)Zbl#: Zbl 1149.42013In 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.The work of the first and fourth author was supported by (CMUC) Department of Mathematics, University of Coimbra. The second author would like to thank Unidade de investigação (Matemática e Aplicações) da Universidade de Aveiro. The work of the third author was supported by Dirección General de Investigación (Ministerio de Educación y Ciencia) of Spain under Grant MTM 2006-13000-C03-02. The work of M.N. Rebocho was supported by FCT, Fundação para a Ciência e Tecnologia, with Grant ref. SFRH/BD/25426/2005.Publicad