On the Blaschke Factors in Polydisk

The purpose of this work is to construct a multidimensional analogue of the Blaschke factors. The relevance of the construction of this analogue was prompted by a recent joint article by Alpay and Yger devoted to the multidimensional interpolation theory for functional spaces in special Weyl polyhedra. By such a factor we understand a set of special inner rational functions in a unit polydisk. We construct inner rational functions for the case of three complex variables, in particular, using the Lee-Yang polynomial from the theory of phase transitions in statistical mechanics.