Some results on the relationship between two-dimensional behaviors decompositions and the factor skew-primeness property
type: Item
instance of: scholarly article
title: Some results on the relationship between two-dimensional behaviors decompositions and the factor skew-primeness property
zbMATH Open document ID: 1035.93038
DOI: 10.1023/A:1015860413906
author: Mauro Bisiacco
author: Maria Elena Valcher
published in: Multidimensional Systems and Signal Processing
publication date: 2002-08-26T00:00:00Z
review text: The aim of the paper is to extend the autonomous/controllable decomposition for linear shift-invariant complete 2D behaviors to a more general setting: given a 2D complete behavior \(\mathfrak{B}\) and one of its sub-behaviors \(\mathfrak{B}_{1}\), some conditions are emphasized under which a complete behavior \(\mathfrak{B}_{2}\) can be found such that \(\mathfrak{B}=\mathfrak{B}_{1}+\mathfrak{B}_{2}\) and \(\mathfrak{B}_{1}\cap\mathfrak{B}_{2}\) is finite dimensional and autonomous. The starting point is represented by a previous paper of the authors in which necessary and sufficient conditions for the more restrictive direct sum decomposition \(\mathfrak{B}=\mathfrak{B}_{1}\oplus\mathfrak{B}_{2}\) were established. The main result (Theorem 4.1) states one-way (necessary or sufficient) conditions for the decomposition \(\mathfrak{B}=\mathfrak{B}_{1}+\mathfrak{B}_{2}\) above, conditions which are related to the factor skew-primeness property of some suitable matrix pairs. Some counterexamples are used to show that these conditions are not two-way. Some special situations are emphasized in which these conditions are necessary and sufficient.
reviewed by: Valeriu Prepeliţă
Mathematics Subject Classification ID: 93C35
Mathematics Subject Classification ID: 93B11
Mathematics Subject Classification ID: 93B25
Mathematics Subject Classification ID: 93C05
zbMATH DE Number: 1788476
zbMATH Keywords: complete two-dimensional behavior
zbMATH Keywords: behavior decomposition
zbMATH Keywords: factor skew-primeness
zbMATH Keywords: two-sided diophantine equations
zbMATH Keywords: 2D behaviors
MaRDI profile type: Publication
full work available at URL: a:1015860413906
OpenAlex ID: W1560403998
description: scientific article; zbMATH DE number 1788476