2004/06/30 by Victor Katsnelson, Dan Volok
Mathematics · #math.CA #math.AP #msc:47A56 #msc:34M55
published as Operator Theory, System Theory And Scattering Theory: Multidimensional Generalizations, Operator Theory: Advances and Applications, vol. 157 (2005), pp. 165 - 203 · added appendix
arxiv created 2005/06/18 · arxiv updated 2009/12/01
In this second article of the series we study holomorphic families of generic rational matrix functions parameterized by the pole and zero loci. In particular, the isoprincipal deformations of generic rational matrix functions are proved to be isosemiresidual. The corresponding rational solutions of the Schlesinger system are constructed and the explicit expression for the related tau function is given. The main tool is the theory of joint system representations for rational matrix functions with prescribed pole and zero structures.