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

Katsnelson, Victor; Volok, Dan

doi:10.1007/3-7643-7303-2_6

Cited by 3 publications

(4 citation statements)

References 11 publications

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“…In our approach this condition can fail for x = ∞. Thus our theory can be applied to the important examples ( see sections [8][9][10] in which classical Fuchsian theory does not work. Remark 1.2.…”

Section: )mentioning

confidence: 98%

“…Example 4.1. V.Katsnelson and D.Volok [10] investigated the case when the point x 0 is a simple pole of W (x) and a holomorphic point of the inverse matrix function W −1 (x). They proved that in this case Proof.…”

Section: Examplesmentioning

confidence: 99%

“…The proposition is proved. According to(10.4) and (10.5) the function D(ξ) can be extended to the entire function D(z). From Proposition 10.1. and relation (10.29) we obtain the assertions.…”

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confidence: 99%

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Meromorphic solutions of linear differential systems, Painlevé type functions

Sakhnovich¹

2007

Operators and Matrices

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Abstract. We consider the n × n matrix linear differential systems in the complex plane. We find necessary and sufficient conditions under which these systems have meromorphic fundamental solutions. Using the operator identity method we construct a set of systems which have meromorphic solutions. We prove that the well known operator with the sine kernel generates a class of meromorphic Painlevé type functions. The fifth Painlevé function belongs to this class. Hence we obtain a new and simple proof that the fifth Painlevé function is meromorphic. (2000): 34M05, 34M55, 47B38. Mathematics subject classification

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Section: )mentioning

confidence: 98%

Section: Examplesmentioning

confidence: 99%

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Meromorphic solutions of linear differential systems, Painlevé type functions

Sakhnovich¹

2007

Operators and Matrices

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“…These system realizations, in turn, play a certain role in the solution of the original problem (See, for example, [AG]). The Theory of Isoprincipal Deformations of Rational Matrix-Functions (which is, in particular, a useful tool for investigating rational solutions of Schlesinger systems) is formulated in terms of the Theory of System Realizations (See [KaVo1] and [KaVo2]. For our purposes, the theory developed in [Ka] is most relevant).…”

Section: Introductionmentioning

confidence: 99%

The Schur Algorithm in Terms of System Realizations

Fritzsche

Katsnelson

Kirstein

2009

Characteristic Functions, Scattering Functions and Transfer Functions

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Abstract. The main goal of this paper is to look at the classical Schur algorithm from the perspective of System Theory. We will confine our considerations to rational inner functions. This will allow us to avoid questions involving limits and will enable us to concentrate on the algebraic aspects of the problem at hand. Given a non-negative integer n, we describe all system realizations of a given rational inner function of degree n in terms of an appropriately constructed equivalence relation in the set of all unitary (n + 1) × (n + 1)-matrices. The concept of Redheffer coupling of colligations gives us the possibility to choose a particular representative from each equivalence class. The Schur algorithm for a rational inner function is, consequently, described in terms of the state space representation.

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Deformations of Fuchsian Systems of Linear Differential Equations and the Schlesinger System

Katsnelson

Volok

2006

Math Phys Anal Geom

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

Cited by 3 publications

References 11 publications

Meromorphic solutions of linear differential systems, Painlevé type functions

Meromorphic solutions of linear differential systems, Painlevé type functions

The Schur Algorithm in Terms of System Realizations

Deformations of Fuchsian Systems of Linear Differential Equations and the Schlesinger System

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