Algebraic-geometric operators and Galois differential theory
We show that, by using the Galois differential theory, one can substantially improve the description of algebraic-geometric operators. In particular, we give a complete description of all elementary algebraic-geometric operators, present simple relations for the construction of all second-order operators of this type, and give a criterion for testing the algebraic-geometric properties of a linear differential operator with meromorphic coefficients.
English version (Springer): Ukrainian Mathematical Journal 61 (2009), no. 1, pp 14-29.
Citation Example: Grigorenko N. V. Algebraic-geometric operators and Galois differential theory // Ukr. Mat. Zh. - 2009. - 61, № 1. - pp. 14-27.