2019
Том 71
№ 10

All Issues

Grigorenko N. V.

Articles: 2
Article (Russian)

Algebraic-geometric operators and Galois differential theory

Grigorenko N. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2009. - 61, № 1. - pp. 14-27

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.

Brief Communications (Russian)

Isomonodromic deformations and the differential Galois theory

Grigorenko N. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2007. - 59, № 8. - pp. 1131-1134

We show how a solution of an inverse problem of the differential Galois theory can be used to construct isomonodromic deformations.