Boundary values of ultradistribution solutions to regular-specializable systems (Recent development of micro-local analysis for the theory of asymptotic analysis)
Susumu Yamazaki · Kyoto University Research Information Repository (Kyoto University) · 2013
For any hyperfunction solutions to the regular-specializable system, a boundary value mor- phism is defined by Laurent-Monteiro Fernandes. We announce that this morphism induces a boundary value morphism for extensible ultradistribution solutions to the regular-specializable system under an irregularity condition due toTahara.single equation case, this corresponds to a Fuchsian operator in the sense of Baouendi- Goulaouic [1] with constant characteristic exponents, or equivalently, a regular-singular operator with weak sense due to Kashiwara-Oshima [7] (cf.Oshima [21]).For anyregular-specializable system, its vanishing cycle and nearby cycle in the \ma t hs c r { D} -Module the- ory are defined (see Kashiwara [3], Laurent [13], Maisonobe-Mebkhout [16]).After the results by Kashiwara-Oshima [7] and Oshima [21], for any hyperfunction solutions to a regular-specializable system, Laurent-Monteiro Fernandes ([15], [17], [18]) defined an injective boundary value morphism which takes values in hyperfunction solutions to the nearby cycle of the system.This morphism extends the non-characteristic bound- ary value morphism due to Komatsu-Kawai and Schapira.Note that the solvability is