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Rational Solutions of the Schlesinger System and Isoprincipal Deformations of Rational Matrix Functions II

  • Victor Katsnelson
  • Dan Volok
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 157)

Abstract

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.

Keywords

Isoprincipal isosemiresidual joint system representation Fuchsian system Schlesinger system 

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Copyright information

© Birkhäuser Verlag 2005

Authors and Affiliations

  • Victor Katsnelson
    • 1
  • Dan Volok
    • 2
  1. 1.Department of MathematicsWeizmann Institute of ScienceRehovotIsrael
  2. 2.Department of MathematicsBen Gurion University of the NegevBeer-ShevaIsrael

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