Matrici differenziali (sistemi) ``individuate'' da ogni loro soluzione non nulla

Bratti, Giuliano

Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 559-567

Résumé

A differential matrix has entries in the Weyl algebra $A_n=A$. For the sake of simplicity, $M$ is also the canonical differential system associated with it. Let $A_(p,q)$ be the $A_{(p, q)}$ be the $A_{(p, p)}$-mod$(sx)$ of matrices, $p$ arrows and $q$ columns. Here, we will study the following problems: (P1) Is it true (as in the case of a single differential operator) that the maximality of $A_{(p, p)}M$ in $A(p, q)$ is equivalent to: $\forall M' \in A(p, q)$ such that $M'(u) = M(u) = 0$, $u \neq 0$, we have $M' \in A_{(p, p)}M$? (P2) Describe $M \in A_{(p, q)}$ such that $A_{(p, p)}M$ is maximal in $A_{(p, q)}$.