A Class of Orthogonal Polynomials on the Boundary of an Ellipse

详细

We construct a class of polynomials of one complex variable that are pairwise orthogonal with some weight on the boundary of an ellipse. We prove that an arbitrary λ-holomorphic Hölder function defined in an ellipse is represented as a series with respect to given polynomials. This result is applied to prove the existence and uniqueness of a solution to some functional equation in the ellipse in the Hölder classes.