论文标题
Bessmertnyi实现定理的扩展，用于几个复杂变量的合理函数
Extension of the Bessmertnyi Realization Theorem for Rational Functions of Several Complex Variables
论文作者
论文摘要
我们证明了几个复杂变量的合理函数的实现定理，该定理扩展了Bessmertnyi M.的主要定理，“关于几个复杂变量的有理矩阵函数的实现”，第1卷。操作的134。理论顾问。 Appl。，第157-185页，BirkhäuserVerlag，巴塞尔，2002年。与Bessmertnyi求解大型线性方程系统的方法相反，我们基于Schur补语理论使用了操作员理论方法。这导致了更简单，更“自然”的构建来解决实现问题，因为我们只需要将基本代数操作应用于Schur的补充，例如总和，产品，倒置和构图。我们方法的新颖性是在实现问题中使用Kronecker产品而不是基质产品。因此，我们的合成方法导致了实现问题的解决方案，该方法具有多维系统理论中进一步扩展和应用的潜力，尤其是对于那些与电路，网络和复合材料相关的线性模型。
We prove a realization theorem for rational functions of several complex variables which extends the main theorem of M. Bessmertnyi, "On realizations of rational matrix functions of several complex variables," in Vol. 134 of Oper. Theory Adv. Appl., pp. 157-185, Birkhäuser Verlag, Basel, 2002. In contrast to Bessmertnyi's approach of solving large systems of linear equations, we use an operator theoretical approach based on the theory of Schur complements. This leads to a simpler and more "natural" construction to solving the realization problem as we need only apply elementary algebraic operations to Schur complements such as sums, products, inverses, and compositions. A novelty of our approach is the use of Kronecker product as opposed to the matrix product in the realization problem. As such our synthetic approach leads to a solution of the realization problem that has potential for further extensions and applications within multidimensional systems theory especially for those linear models associated with electric circuits, networks, and composites.
