Interrelations Between the Taylor Coefficients of a Matricial Carathéodory Function and Its Cayley Transform
Abstract The main goal of this paper is to discuss several interrelations between the Taylor coefficients of a q x q matrix-valued Carathéodory function and its Cayley transform which is a q x q matrix Schur function. Both Taylor coefficient sequences are described in terms of corresponding matrix balls. Hereby, we will obtain explicit formulas for the parameters of one matrix ball in terms of the other one. These expressions imply a one-to-one correspondence between central matricial Carathéodory functions and central matricial Schur functions which is established via Cayley transform.