Faber polynomials, Cayley–Hamilton equation and Newton symmetric functions

AbstractWe give an explicit formula for the Faber polynomials and for generalized Faber polynomials introduced by H. Airault and J. Ren in [H. Airault, J. Ren, An algebra of differential operators and generating functions on the set of univalent functions, Bull. Sci. Math. 126 (5) (2002) 343–367]. We introduce a new family of polynomials related to the Faber polynomials of the second kind. This allows us to give a generalized Cayley–Hamilton equation