Orthogonal Polynomials of Sobolev Type on the Unit Circle Original Research Article

In this paper we study algebraic and asymptotic properties of orthogonal polynomials with respect to an inner product in the linear space P of complex polynomials defined by 〈P(z), Q(z)〉 = (φu(P(z), Q(z)) + λ−1P′(a)[formula] where φ(u) is a regular and Hermitian form, λ ∈ R\{0}, and |a| = 1. Major emphasis is given to the positive definite case.