On a new class of realization formulas and their application

Daniel Alpay; Harry Dym

doi:10.1016/0024-3795(95)00602-8

On a new class of realization formulas and their application

Daniel Alpay
, Harry Dym

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

A new set of realization formulas is derived for a class of matrix-valued functions W(λ). These include the standard realization formulas for rational W(λ). Observability, controllability, and minimality are defined and characterized. Conditions for W(λ) to be (J₁, J₂) isometric and/or (J₁, J₂) coisometric with respect to a pair of signature matrices J₁ and J₂ are given in terms of the realizations. Minimal factorizations for square W(λ) are considered, and formulas for the factors are deduced. Associated reproducing kernel spaces (of pairs too) are discussed.

Original language	English
Pages (from-to)	3-84
Number of pages	82
Journal	Linear Algebra and Its Applications
Volume	241-243
DOIs	https://doi.org/10.1016/0024-3795(95)00602-8
State	Published - 1 Jan 1996

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/0024-3795(95)00602-8

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AB - A new set of realization formulas is derived for a class of matrix-valued functions W(λ). These include the standard realization formulas for rational W(λ). Observability, controllability, and minimality are defined and characterized. Conditions for W(λ) to be (J1, J2) isometric and/or (J1, J2) coisometric with respect to a pair of signature matrices J1 and J2 are given in terms of the realizations. Minimal factorizations for square W(λ) are considered, and formulas for the factors are deduced. Associated reproducing kernel spaces (of pairs too) are discussed.

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U2 - 10.1016/0024-3795(95)00602-8

DO - 10.1016/0024-3795(95)00602-8

M3 - Article

AN - SCOPUS:21344444277

SN - 0024-3795

VL - 241-243

SP - 3

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JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

On a new class of realization formulas and their application

Abstract

ASJC Scopus subject areas

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