2012/03/19 by Ramamonjy Andriamifidisoa, Andriamifidisoa, Ramamonjy, Juanito Andrianjanahary +1
Computer Science · Mathematics · #13C60 #14105 #39A10 #47A05 #93B25 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Coding theory and cryptography #Commutative Algebra (math.AC) #Dynamical Systems (math.DS) #FOS: Mathematics #math.AC #math.DS #msc:13C60 #msc:14105 #msc:39A10 #msc:47A05 #msc:93B25
paper · pdf · doi:10.48550/arxiv.1203.4186
31 pages, corrections in the use of ordinals, news proofs and results (including the case of vectors of sequences, referencing to recents publications)
openalex publication_date 2012/03/19 · arxiv created 2021/05/11 · arxiv updated 2021/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 scalar product, which we used to define 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 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.