Zeros of Sobolev orthogonal polynomials on the unit circle

In this contribution, we study the sequences of orthogonal polynomials with respect to the Sobolev inner product, where μ is a nontrivial probability measure supported on the unit circle, α ∈ ℂ, λ ∈ ℝ₊\{0}, and j ∈ ℕ. In particular, we analyze the behavior of their zeros when n and λ tend to infinity, respectively. We also provide some numerical examples to illustrate the behavior of these zeros with respect to α.