A pair of Hermitian regular linear functionals on the unit circle is said to be a -coherent pair if their corresponding sequences of monic orthogonal polynomials and satisfy , , , where . In this contribution, we consider the cases when is the linear functional associated with the Lebesgue and Bernstein-Szegő measures, respectively, and we obtain a classification of the situations where is associated with either a positive nontrivial measure or its rational spectral transformation.
"-Coherent Pairs on the Unit Circle." Abstr. Appl. Anal. 2013 1 - 8, 2013. https://doi.org/10.1155/2013/307974