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

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

2003-04-08

arxiv.org/abs/math/0304108v3

Current Trends in Operator Theory and its Applications, Operator Theory: Advances and Applications, vol. 149 (2004), pp. 291-3

Mathematics

Classical Analysis and ODEs

extended version

Scientific paper

In the present paper we discuss the general facts, concerning the Schlesinger system: the (\tau)-function, the local factorization of solutions of Fuchsian equations and holomorphic deformations. We introduce the terminology "isoprincipal" for the deformations of Fuchsian equations with general (not necessarily non-resonant) matrix coefficients, corresponding to solutions of the Schlesinger system.

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