[en] We prove that any perfect complex of $D^{\infty}-modules may be
reconstructed from its holomorphic solution complex provided that we keep
track of the natural topology of this last complex. This is to be compared
with the reconstruction theorem for regular holonomic D-modules which follows
from the well-known Riemann-Hilbert correspondence.
M. Artin, A. Grothendieck, and J.-L. Verdier, eds., Théorie des topos et cohomologie étale des schémas, Tome 1: Théorie des topos, Séminaire de Géométrie Algébrique du Bois-Marie (SGA 4), Lecture Notes in Math. 269, Springer-Verlag, Berlin, 1972.
M. Artin and B. Mazur, Etale Homotopy, Lecture Notes in Math. 100, Springer-Verlag, Berlin, 1969.
A. Grothendieck, Sur certains espaces de fonctions holomorphes, I, J. Reine Angew. Math. 192 (1953), 35-64.
A. Grothendieck, Sur certains espaces de fonctions holomorphes, II, J. Reine Angew. Math. 192 (1953), 77-95.
R. Ishimura, Homomorphismes du faisceau des germes de fonctions holomorphes dans lui-même et opérateurs différentiels, Mem. Fac. Sci. Kyushu Univ. Ser. A 32 (1978), 301-312.
M. Kashiwara, The Riemann-Hilbert problem for holonomic systems, Publ. Res. Inst. Math. Sci. 20 (1984), 319-365.
G. Kothe, Dualitat in der Funktionentheorie, J. Reine Angew. Math. 191 (1953), 30-49.
G. Kothe, Topological Vector Spaces, I, Grundlehren Math. Wiss. 159, Springer-Verlag, New York, 1969.
Z. Mebkhout, Une autre équivalence de catégories, Compositio Math. 51 (1984), 63-88.
V. P. Palamodov, Homological methods in the theory of locally convex spaces (in Russian), Uspekhi Mat. Nauk 26, no. 1, (1971), 3-65
V. P. Palamodov, Homological methods in the theory of locally convex spaces (in Russian), English transl. in Russian Math. Surveys 26 (1971), 1-64.
A. Pietsch, Nuclear Locally Convex Spaces, Ergeb. Math. Grenzgeb. (3) 66, Springer-Verlag, New York, 1972.
F. Prosmans, Algèbre homologique quasi-abélienne, Mémoire de DEA, 1995, available from http://www-math.univ-paris13.fr/'prosmans/.
F. Prosmans, Derivedlimits in quasi-abelian categories, preprint, 1998, to appear in Bull. Soc. Roy. Sci. Liège, available from http://www-math.univ-paris13.fr/'prosmans/.
F. Prosmans, Derived projective limits of topological abelian groups, J. Funct. Anal. 162 (1999), 135-177.
F. Prosmans, Derived categories for functional analysis, to appear in Publ. Res. Inst. Math. Sci., available from http://www-math.univ-paris13.fr/'prosmans/.
M. Sato, T. Kawai, and M. Kashiwara, “Microfunctions and pseudo-differential equations” in Hyperfunctions and Pseudo-Differential Equations (Katata, 1971), ed. H. Komatsu, Lecture Notes in Math. 287, Springer-Verlag, Berlin, 1973, 265-529.
J.-P. Schneiders, Quasi-abelian categories and sheaves, Mém. Soc. Math. France (N.S.) 76 (1999). 10927-49256
E. M. Chirka, Complex Analytic Sets (in Russian), “Nauka”, Moscow, 1985; English transl. in Math. Appl. (Soviet Ser.) 46, Kluwer Acad. Publ., Dordrecht, 1989.
E. M. Chirka and E. L. Stout, “Removable singularities in the boundary” in Contribu-tions to Complex Analysis and Analytic Geometry, Aspects Math. E 26, Vieweg, Braunschweig, 1994, 43-104.
A. Dimca, private communication.
A. V. Domrin, On the spanning of maximally complex cycles by CR-submanifolds (in Russian), Mat. Zametki 60 (1996), 776-777
A. V. Domrin, On the spanning of maximally complex cycles by CR-submanifolds (in Russian), English transl. in Math. Notes 60 (1996), 582-583.
J. Duval, “Surfaces convexes dans un bord pseudoconvexe” in Colloque d'Analyse Complete et Géométrie (Marseille, 1992), Astérisque 217, Soc. Math. France, Mon-trouge, 1993, 6, 103-118.
F. Forstneric, Regularity of varieties in strictly pseudoconvex domains, Publ. Mat. 32 (1988), 145-150.
F. Forstneric and E. L. Stout, A new class of polynomially convex sets, Ark. Mat. 29 (1991), 51-62.
M. Golubitsky and V. Guillemin, Stable Mappings and Their Singularities, Grad. Texts in Math. 14, Springer-Verlag, New York, 1973.
M. L. Gromov, Convex integration of differential relations, I (in Russian), Izv. Akad. Nauk SSSR Ser. Mat. 37 (4), 329-343
M. L. Gromov, Convex integration of differential relations, I (in Russian) English transl. in Math. USSR-Izv. 7 (1973), 329-343.
M. W. Hirsch, Differential Topology, Grad. Texts in Math. 33, Springer-Verlag, New York, 1976.
B. Joricke, Removable singularities of CR-functions, Ark. Mat. 26 (1988), 117-143.
B. Joricke, Boundaries of singularity sets, removable singularities, and CR-invariant subsets of CR-manifolds, J. Geom. Anal. 9 (1999), 257-300.
B. Joricke, Removable singularities of Lp CR-functions on hypersurfaces, J. Geom. Anal. 9 (1999), 429-456.
G. Lupacciolu, Characterization of removable sets in strongly pseudoconvex boundaries, Ark. Mat. 32 (1994), 455-473.
E. L. Stout, “Removable singularities for the boundary values of holomorphic functions” in Several Complex Variables: Proceedings of the Special YearHeld at the Mittag-Leffler Institute (Stockholm, 1987/1988), Math. Notes 38, Princeton Univ. Press, Princeton, 1993, 600-629.
J. Wermer, On a domain equivalent to the bidisk, Math. Ann. 248 (1980), 193-194.