Asymptotic behaviour of Sobolev orthogonal polynomials on the unit circle

In this contribution, we deal with analytic properties of sequences of polynomials orthogonal with respect to a Sobolev-type inner product, where μ is a non-trivial probability measure supported on the unit circle. We focus our attention on the outer relative asymptotics of these polynomials in terms of those associated with the measure μ. The behaviour of their zeros in terms of the parameter λ is studied in some illustrative examples.