Victor Katsnelson, Dan Volok
Published 2004-06-24, updated 2005-06-18Version 2
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.
Comments: added appendix
Journal: Operator Theory, System Theory And Scattering Theory: Multidimensional Generalizations, Operator Theory: Advances and Applications, vol. 157 (2005), pp. 165 - 203
Rational Solutions of the Schlesinger System and Isoprincipal Deformations of Rational Matrix Functions I
The Schlesinger System and the Riemann-Hilbert Problem
Deformations of Fuchsian Systems of Linear Differential Equations and the Schlesinger System
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