Carathéodory-Fejér interpolation on polydisks (Q1574774)

The Carathéodory-Fejér problem consists of the question of whether a polynomial can be extended with higher degree terms to a convergent series from the unit disc into itself. The solvability of this problem is equivalent to the positive semi-definiteness of an associated Toeplitz type matrix which depends only on the coefficients of the original polynomial. In this note the authors propose a solution to the Carathéodory-Fejér problem in the bidisk via Agler's version of the Herglotz-Nevanlinna formula.