确定离散多维系统的粗网格
The coarsest lattice that determines a discrete multidimensional system
摘要：
离散多维系统是定义在格$\Z^n$上的线性偏差分方程组的解的集合。本文表明，它是由一个独特的粗子格，在这个意义上，该系统的解决方案，在这个子格确定的解决方案$\Z^n$，因此，它是正确的定义域的离散系统。反过来，定义子格由对称性的伽罗瓦群确定，这些对称性使定义系统的方程保持不变。这些结果在理解系统的性质，如可控性和自治性，并在其订单减少中找到应用。
英文摘要：
A discrete multidimensional system is the set of solutions to a system of linear partial difference equations defined on the lattice $\Z^n$. This paper shows that it is determined by a unique coarsest sublattice, in the sense that the solutions of the system on this sublattice determine the solutions on $\Z^n$; it is therefore the correct domain of definition of the discrete system. In turn, the defining sublattice is determined by a Galois group of symmetries that leave invariant the equations defining the system. These results find application in understanding properties of the system such as controllability and autonomy, and in its order reduction.
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