Integer invariants of linear differential systems

Author: Vakhtang Lomadze
Keywords: Linear system, Wiener-Hopf functions, jet-spaces
Annotation:

A linear differential system B is a set that is representable as the solution set of a system of linear constant coefficient partial differential equations. We associate to B a sequence of integer functions (a1, . . . , al), ai : [1, pi] → Z+. Here l is the "homological" dimension. We call a1, . . . , al the Wiener-Hopf functions of B. For every d ≥ 0, let B|d denote the space of d-jets of the trajectories belonging to B. We then have an inverse system B|0 ← B|1 ← B|3 ← • • • ← B|d ← • • • ., which is important as it completely determines the whole B. We express the dimensions of the jet-spaces by means of the Wiener-Hopf functions.