Year: 2025
Type: preprint
Abstract: We generalize the framework of discrete algebraic dynamical systems \cite{Andriamifidisoa2014} to Laurent polynomials and series over \(\Z^r\), enabling the modeling of bidirectional discrete systems. By redefining the spaces \(\Dprime\) and \(\Aprime\), introducing a bilinear mapping (defined as the scalar product in Section 3), and extending the shift operator, we preserve the duality and adjoint properties of \cite{Andriamifidisoa2014}. These properties are rigorously proved and illustrated through examples and a data processing case study on bidirectional sequence transformations. In contrast to Oberst \cite{Ob90}, our algebraic approach emphasizes the structure of Laurent series, providing a streamlined framework for multidimensional systems. This work addresses an open question from \cite{Andriamifidisoa2014} and has applications in multidimensional data processing, such as image filtering and control theory.
Source: arXiv (Cornell University)
Authors: Aandriamifidisoa, Ramamonjy, Saindou, Loukman Ben
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6948194389
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