Discrete linear Algebraic Dynamical Systems
Abstract
The vector space of the multi-indexed sequences over a field and the vector space of the sequences with finite support are dual to each other, with respect to a \textit{scalar product}, which we used to define \textit{orthogonals} in these spaces. The closed subspaces in the first vector space are then the orthogonals of subsets in the second space. Using power series and polynomials, we prove that the \textit{polynomial operator in the shift} which U. Oberst and J. C. Willems have introduced to define time invariant discrete linear dynamical systems is the functorial adjoint of the polynomial multiplication. These results are generalized to the case of vectors of sequences and vectors of power series and polynomials. We end this paper by describing discrete linear algebraic dynamical systems.
Cite
@article{arxiv.1203.4186,
title = {Discrete linear Algebraic Dynamical Systems},
author = {Ramamonjy Andriamifidisoa and Juanito Andrianjanahary},
journal= {arXiv preprint arXiv:1203.4186},
year = {2021}
}
Comments
31 pages, corrections in the use of ordinals, news proofs and results (including the case of vectors of sequences, referencing to recents publications)