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

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

2004-06-24

arxiv.org/abs/math/0406489v2

Operator Theory, System Theory And Scattering Theory: Multidimensional Generalizations, Operator Theory: Advances and Applicat

Mathematics

Classical Analysis and ODEs

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Scientific paper

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.

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