NDLI: Finite-Memory Systems

Content Provider	Springer Nature Link
Author	Fasoli, Maria Alessandra
Copyright Year	1998
Abstract	Let K be a field, k and n positive integers and let $$A_1 , \ldots ,A_k {\text{ be }}n \times n - $$ matrices with coefficients in K. For any function $$g\pmb{: }\Gamma : = \left\{ {t: = (t_1 , \ldots ,t_k )} \right. \in \mathbb{N}^k \left\| {\left. {t_1 t_2 \ldots t_k = 0} \right\}} \right. \to K^n $$ there exists a unique solution $$x:\mathbb{N}^k \to K^n $$ of the system of difference equations $$\left( \right)x(t_1 + 1, \ldots ,t_k + 1) = $$ $$ = \sum\nolimits_{j = 1}^k {A_j x} (t_1 + 1, \ldots ,t_{j - 1} + 1,t_j ,t_{j + 1} + 1, \ldots ,t_k + 1)$$ defined by the matrix-k-tuple $$(A_1 , \ldots ,A_k ) \in M(n;K)^k $$ such that $$x_{\left\| \Gamma \right.} = g$$ . The system $$\left( \right)$$ is called “finite-memory system” iff for every function g with finite support the values $$x(t_1 , \ldots ,t_k )$$ are 0 for sufficiently big $$t_1 + \cdots + t_k $$ . In the case $$k = 2,K = \mathbb{R}$$ , these systems and the corresponding matrix-k-tuples have been studied in bis, fm, fmv, fv1, fv, fz. In this paper I generalize these results to an arbitrary positive integer k and to an arbitrary field K.
Starting Page	291
Ending Page	306
Page Count	16
File Format	PDF
ISSN	09236082
Journal	Multidimensional Systems and Signal Processing
Volume Number	9
Issue Number	3
e-ISSN	15730824
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	1998-01-01
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Artificial Intelligence (incl. Robotics) Electronic and Computer Engineering Signal, Image and Speech Processing Circuits and Systems
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Artificial Intelligence Signal Processing Information Systems Computer Science Applications Software Hardware and Architecture

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