Remarks on boundary values for temperate distribution solutions to regular-specializable systems (Q2902440)

The notion of a regular-specializable system was defined by \textit{M. Kashiwara} [Lect. Notes Math. 1016, 134--142 (1983; Zbl 0566.32022)], and boundary value problems for this kind of systems have been study by several authors as it is well reported in the introduction and bibliography of this paper. NEWLINENEWLINENEWLINE This work of Yamasaki uses Kashiwara's functor of moderate cohomology and its microlocalization (due to Andronikof) as well as Kashiwara-Schapiras's algebraic and geometric tools to consider boundary value problems for temperate distribution solutions to regular-specializable systems and it is proved that the boundary value morphism of \textit{T. Monteiro Fernandes} [Compos. Math. 81, No. 2, 121--142 (1992; Zbl 0754.58034); C. R. Acad. Sci., Paris, Sér. I 318, No. 10, 913--918 (1994; Zbl 0810.58037)] induces the boundary value morphism for temperate distribution solutions to these systems. Moreover, it is shown that this morphism is bijective if the system satisfies certain hyperbolicity conditions. NEWLINENEWLINENEWLINE The paper also includes a very useful appendix where the definition of a (regular-) specializable system as well as the construction of its vanishing and nearby cycle modules are recalled, providing an overview of the main results of this theory, that appear to be somewhat dispersed by the bibliography of reference.