Some properties of functions with nonzero order n divided difference

Abstract

We consider the properties of functions of class Kn(D). This class consists of analytic functions F(z) in a domain D whose nth divided difference does not vanish in D. We study some relation of functions of class Kn(D) to Chebyshev systems, consider a few properties of an operator related to a fractional linear transformation of the unit disk, and estimate Taylor series coefficients.