(1,1) -coherent pairs on the unit circle

A pair (U,V) of Hermitian regular linear functionals on the unit circle is said to be a (1,1)-coherent pair if their corresponding sequences of monic orthogonal polynomials {φn(x)}n≥0 and {ψn(x)}n≥0 satisfy φn[1](z)+anφn-1[1](z)=ψn(z)+bnψn-1(z), an≠0, n≥1, where φn[1](z)=φn+1′(z)/(n+1). In this contribution, we consider the cases when U is the linear functional associated with the Lebesgue and Bernstein-Szegod measures, respectively, and we obtain a classification of the situations where V is associated with either a positive nontrivial measure or its rational spectral transformation.