Algebraic-geometric operators and Galois differential theory

  • N. V. Grigorenko


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.
How to Cite
Grigorenko, N. V. “Algebraic-Geometric Operators and Galois Differential Theory”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, no. 1, Jan. 2009, pp. 14-27,
Research articles