An algebra of differential operators and generating functions on the set of univalent functions

AbstractWith a method close to that of Kirillov [4], we define sequences of vector fields on the set of univalent functions and we construct systems of partial differential equations which have the sequence of the Faber polynomials (Fn) as a solution. Through the Faber polynomials and Grunsky coefficients, we obtain the generating functions for some of the sequences of vector fields