Meromorphic Matrix Research Articles

Multiplicities of Nonsimple Zeros of Meromorphic Matrix Functions of the Class Nn×nx

Multiplicities of Nonsimple Zeros of Meromorphic Matrix Functions of the Class <i>N</i>^{<i>n</i>×<i>n</i>}_x

Explicit N-soliton solution of the modified nonlinear Schrödinger equation.

By means of the technique of determinant calculation, an explicit N-soliton solution of the modified nonlinear Schr\odinger equation is obtained for arbitrary N using the method of a meromorphic transformation matrix. The final expression is written in a form suitable for practical needs. Its expected asymptotic behavior is derived.

Method of meromorphic matrix of transformation for giving soliton solutions of the modified nonlinear Schrödinger equation

Abstract A method on the Darboux transformation in the form of a pole expansion is presented for finding soliton solutions of the modified nonlinear Schrodinger equation.

Equivalence Between Open-Loop and Closed-Loop Invariance for Infinite-Dimensional Systems: A Frequency Domain Approach

In this paper the relation between various system invariance concepts is considered, and it is proved that open- and closed-loop invariance are equivalent concepts. Using this equivalence the author investigates the existence of the largest closed-loop invariant subspace, and derives necessary and sufficient conditions such that the largest open-loop invariant subspace is equal to the largest closed-loop invariant subspace. If this equality holds, then the solvability of the disturbance decoupling problem (DDP) is equivalent to the solvability of a meromorphic matrix equation.

Factorization of a class of meromorphic matrix valued functions

Factorization of a class of meromorphic matrix valued functions

Minimal factorization of meromorphic matrix functions in terms of local data

Description de tous les diviseurs minimaux en un point donne d'une fonction matricielle meromorphe en termes de paires spectrales locales et de matrice de couplage locale

Interpolation problems of Pick-Nevanlinna and Loewner types for meromorphic matrix functions: Parametrization of the set of all solutions

We consider a general matrix version of a Pick-Loewner interpolation problem on the closed unit disk. Solutions are allowed to have a finite numberl of free poles in the open disk. We show that the smallestl for which a solution to the problem exists is the number of negative eigenvalues of an appropriately defined “Pick matrix,” and for this value ofl we obtain a linear fractional map parametrization of the class of all solutions. The idea is to adapt the Grassmannian approach involving Krein space geometry and invariant subspace representations of the authors; this was successful previously for the case where all interpolating points are inside the disk. Also an appendix includes an errata to earlier work together with simplified proofs.

Interpolation and local data for meromorphic matrix and operator functions

The main result of this paper is a generalization of the Mittag-Leffler theorem to matrix and operator valued meromorphic functions. Namely, a meromorphic matrix or operator valued function is constructed when the singular parts of the function and if its inverse are given in all singular points (which are assumed to be isolated). The paper contains also interpolation theorems based on other forms of local data (Jordan chains from left and right of the function and its inverse). An analysis of the local data, which is used in the proofs of these theorems is also included.

Hamiltonian Hierarchies on Semisimple Lie Algebras

A recursion formula is described which generates infinite hierarchies of completely integrable Hamiltonian systems of nonlinear partial differential equations. These equations govern the evolution of a function u of x, t which takes its values in a semisimple Lie algebra. A Hamiltonian for the hierarchy is given in terms of a meromorphic connection matrix.

Interpolation problems of Pick-Nevanlinna and Loewner types for meromorphic matrix functions

Classical interpolation problems are concerned with the problem of finding an analytic function on the unit disk bounded by one which takes on prescribed values at certain prescribed points inside the disk (Pick-Nevanlinna) or on the boundary of the disk (Loewner). We consider the problem for matrix-valued functions having as many asl poles (l a nonnegative integer) inside the disk but still uniformly bounded by one on the boundary of the disk. Our technique is an adaptation of that of Sz.-Nagy and Koranyi to spaces with an indefinite inner product. The problem arises in the broadband matching problem for electrical circuits and certain multichannel scattering problems in physics.

A sign characteristic for selfadjoint meromorphic matrix functions

We introduce the notion of sign characteristic for selfadjoint meromorphic matrix functions which generalizes this notion for matrix polynomials introduced by the authors in [4]. The purpose of this paper is to show equivalence of various definitions of the sign characteristic for meromorphic matrix functions