V. N. Chetverikov
Invertible linear differential operators on two-dimensional manifolds
Preprint series: ESI preprints

MSC:

35A30 Geometric theory, characteristics, transformations, See also {58G35, 58G37}

47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)

47D03 (Semi)groups of linear operators, {For nonlinear operators, See 47H20; See also 20M20}

58G35 Invariance and symmetry properties, See also {35A30}

Abstract: In case of two independent variables invertible linear differential
operators structure is described. It is proved that a two-sided
invertible operator can be written as a composition of triangular
invertible operators in the stable sense. The form to which a
left-invertible operator can be reduced by composing it with
triangular operators is given.

Keywords: invertible differential operators, transformations, triangular operators