CURVE TEST FOR ENHANCED IND-SHEAVES AND HOLONOMIC D-MODULES, I

Recently, the Riemann-Hilbert correspondence was generalized to the context of holonomic D-modules by A. D'Agnolo and M. Kashiwara. Namely, they proved that their enhanced de Rham functor induces a fully faithful embedding of the derived category of cohomologically holonomic complexes of D-modules into the derived category of complexes of cohomologically R-constructible enhanced ind-sheaves. In this series of papers, we study a condition when a complex of R-constructible enhanced indsheaves K is induced by a cohomologically holonomic complex of D-modules. It is our goal to characterize such K in terms of the restriction of K to holomorphic curves. In this paper (part I), as a preliminary, we shall study some issues for multi-sets of subanalytic functions.