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Matrix-valued Functions (matrix-valued + function)

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Mathematics and Statistics100%

Selected Abstracts

Generalized factorization for N×N Daniele,Khrapkov matrix functions

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2001
M. C. Cāmara
Abstract A generalization to N×N of the 2×2 Daniele,Khrapkov class of matrix-valued functions is proposed. This class retains some of the features of the 2×2 Daniele,Khrapkov class, in particular, the presence of certain square-root functions in its definition. Functions of this class appear in the study of finite-dimensional integrable systems. The paper concentrates on giving the main properties of the class, using them to outline a method for the study of the Wiener,Hopf factorization of the symbols of this class. This is done through examples that are completely worked out. One of these examples corresponds to a particular case of the motion of a symmetric rigid body with a fixed point (Lagrange top). Copyright © 2001 John Wiley & Sons, Ltd. [source]

On realization of the Kre,n,Langer class N, of matrix-valued functions in Pontryagin spaces

MATHEMATISCHE NACHRICHTEN, Issue 10 2008
Yury Arlinski
Abstract In this paper the realization problems for the Kre,n,Langer class N, of matrix-valued functions are being considered. We found the criterion when a given matrix-valued function from the class N, can be realized as linear-fractional transformation of the transfer function of canonical conservative system of the M. Livsic type (Brodskii,Livsic rigged operator colligation) with the main operator acting on a rigged Pontryagin space ,, with indefinite metric. We specify three subclasses of the class N, (R) of all realizable matrix-valued functions that correspond to different properties of a realizing system, in particular, when the domains of the main operator of a system and its conjugate coincide, when the domain of the hermitian part of a main operator is dense in ,,. Alternatively we show that the class N, (R) can be realized as transfer matrix-functions of some canonical impedance systems with self-adjoint main operators in rigged spaces ,,. The case of scalar functions of the class N, (R) is considered in details and some examples are presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]