Coherent pairs of linear functionals on the unit circle

• Author(s): Branquinho, A. ; Moreno, A. Foulquié ; Marcellán, F. ; Rebocho, M. N.
• Date: 2008
• Persistent ID: http://hdl.handle.net/10316/4581
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): Orthogonal polynomials; Differential equations; Three-term recurrence relations; Measures on the unit circle; Hermitian functionals
• Document Type: Article
• Language: English

Description

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 ([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. http://www.sciencedirect.com/science/article/B6WH7-4S2MJ0D-1/1/61050bb3811832f373ff40a48b7461d1