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Zbl 0869.58050
D'Agnolo, Andrea; Zampieri, Giuseppe
Microlocal direct images of simple sheaves with applications to systems with simple characteristics. (English)
[J] Bull. Soc. Math. Fr. 123, No.4, 605-637 (1995). ISSN 0037-9484

Summary: We state a hypoellipticity result in the framework of microlocal boundary value problems (which has to be compared with the analogous results of {\it M. Sato}, {\it T. Kawai} and {\it M. Kashiwara} [Hyperfunctions pseudo-diff. equations, Proc. Conf. Katata 1971, Lect. Notes Math. 287, 263-529 (1973; Zbl 0277.46039)] and {\it M. Kashiwara} and {\it P. Schapira} [Invent. Math. 82, 579-592 (1985; Zbl 0626.58028)] at the interior). More precisely, let ${\cal M}$ be a system of microdifferential equations with simple characteristics on a complex manifold $X$, and let $\Lambda_i$ $(i=1,2)$ be a pair of real Lagrangian submanifolds of $T^*X$. Denote by ${\cal C}_{\Lambda_i}$ the associated complexes of microfunctions. If the pair $(\Lambda_1,\Lambda_2)$ is ``positive'', we prove the injectivity of the natural ``restriction'' morphism $${\cal E}xt^j_{{\cal E}_X}({\cal M},{\cal C}_{\Lambda_2})\to{\cal E}xt^n_{{\cal E}_X}({\cal M},{\cal C}_{\Lambda_1})$$ between solution sheaves, where $j$ is the first possibly non-vanishing degree of the cohomology.

MSC 2000:: *58J15 Relations with hyperfunctions
32C38 Sheaves of differential operators (analytic spaces)

Keywords: microlocal direct images; simple sheaves; microlocal boundary value problems; microdifferential equations; simple characteristics

Citations: Zbl 0277.46039; Zbl 0626.58028

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