Algebraic-geometric operators and Galois differential theory - Grigorenko, N. V. (Ukrains’kyi Matematychnyi Zhurnal, 2009)
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.