Some properties of functions with nonzero order $n$ divided difference

We consider the properties of functions of class $K_n(D)$. 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 $K_n(D)$ 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.