The injectivity of the canonical signal module for multidimensional linear systems of difference equations with variable coefficients - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Multidimensional Systems and Signal Processing Année : 2015

The injectivity of the canonical signal module for multidimensional linear systems of difference equations with variable coefficients

B Marinescu
  • Fonction : Auteur
  • PersonId : 980901
U Oberst
  • Fonction : Auteur

Résumé

We consider discrete behaviors with varying coefficients. Our results are new also for one-dimensional systems over the time-axis of natural numbers and for varying coefficients in a field, we derive the results, however, in much greater generality: Instead of the natural numbers we use an arbitrary submonoid N of an abelian group, for instance the standard multidimensional lattice of r-dimensional vectors of natural numbers or integers. We replace the base field by any commuta-tive self-injective ring F, for instance a direct product of fields or a quasi-Frobenius ring or a finite factor ring of the integers. The F-module W of functions from N to F is the canonical discrete signal module and is a left module over the natural associated noncommutative ring A of difference operators with variable coefficients. Our main result states that this module is injective and therefore satisfies the fundamental principle: An inhomogeneous system of linear difference equations with variable coefficients has a solution if and only if the right side satisfies the canoni-cal compatibility conditions. We also show that for the typical cases of partial difference equations and in contrast to the case of constant coefficients the A-module W is not a cogenerator. We also generalize the standard one-dimensional theory for periodic coefficients to the multidimensional situation by invoking Morita equivalence.
Fichier principal
Vignette du fichier
R48bis.pdf (419.47 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02368215 , version 2 (22-12-2016)
hal-02368215 , version 1 (20-11-2019)

Identifiants

Citer

H Bourlès, B Marinescu, U Oberst. The injectivity of the canonical signal module for multidimensional linear systems of difference equations with variable coefficients. Multidimensional Systems and Signal Processing, 2015, ⟨10.1007/s11045-015-0331-x⟩. ⟨hal-02368215v1⟩
319 Consultations
173 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More