On a class of linear differential operators of infinite order with finite index (Q1093081)

Some conditions on a linear differential operator P which guarantees the finiteness of the dimensions of the kernel and the cokernel of the map \(P: {\mathcal O}_{{\mathbb{C}}^ n,0}\to {\mathcal O}_{{\mathbb{C}}^ n,0}\), where \({\mathcal O}_{{\mathbb{C}}^ n,0}\) denotes the germ at the origin of the sheaf \({\mathcal O}_{{\mathbb{C}}^ n}\) of holomorphic functions on \({\mathbb{C}}^ n\), are presented. These results are a generalization of Bony-Schapira results to the infinite-order case.