Field extensions and extensions of linear differential operators

Let K subset of R subset of P be a tower of fields, N be a P-module, and Delta:R --> N be a K-linear differential operator. The aim of this paper is to investigate whether the operator Delta has an extension to P, i.e. if these exists a differential operator Delta':P --> N such that Delta'\(R) = Delta. The results of this paper were published in Russian in Mat. Zametki 30(2) (1981), 237-248.