Extension of the Bessmertnyĭ Realization Theorem for Rational Functions of Several Complex Variables

We prove a realization theorem for rational functions of several complex variables which extends the main Bessmertnyĭ (in: Alpay, Gohberg, Vinnikov (eds) Interpolation Theory, Systems Theory and Related Topics. Operator Advances Applications vol 134. Birkhauser Verlag, Basel, pp 157–185, 2002). In contrast to Bessmertnyĭ’s approach solving large systems linear equations, we use an operator theoretical based on theory Schur complements. This leads simpler more “natural” construction problem as need only apply elementary algebraic operations complements such sums, products, inverses, compositions. A novelty our is Kronecker product opposed matrix in problem. As synthetic solution that has potential further extensions applications within multidimensional especially those models associated with electric circuits, networks, composites.