Invertible linear ordinary differential operators

We consider invertible linear ordinary differential operators whose inversions are also differential operators. To each such operator we assign a numerical table. These tables are described in the elementary geometrical language. The table does not uniquely determine the operator. To define this operator uniquely some additional information should be added, as it is described in detail in this paper. The possibility of generalization of these results to partial differential operators is also discussed. (C) 2016 Elsevier B.V. All rights reserved.