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Algebraic-geometric operators and Galois differential theory

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Ukrainian Mathematical Journal Aims and scope

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.

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Authors and Affiliations

  1. Kiev National Agricultural University, Kiev, Ukraine

    N. V. Grigorenko

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  1. N. V. Grigorenko
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 1, pp. 14–27, January, 2009.

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Grigorenko, N.V. Algebraic-geometric operators and Galois differential theory. Ukr Math J 61, 14–29 (2009). https://doi.org/10.1007/s11253-009-0200-6

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  • DOI: https://doi.org/10.1007/s11253-009-0200-6

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