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Elliptic boundary value problems in the space of distributions

  • Emmanuel Andronikof
  • Nobuyuki Tose

Abstract

Elliptic boundary value problems have their own long history. For the general system they were, however, first clearly fomulated microlocally by M. Kashiwara and T. Kawai [K-K]. Their theorem has enjoyed many applications, for example, to solvability of operators of simple characteristics, hypoelliptic operators, and tangential Cauchy-Riemann systems. The theorem does not give, however, much information if we restrict ourselves in the space of distributions. This note aims at giving an analogous theorem of Kashiwara-Kawai type in case function spaces are tempered. See Theorem 3 in Section 1 for the main theorem. By this theorem, we can obtain many application to distribution boundary values of holomorphic functions (e.g. M. Uchida[U]).

Keywords

Elliptic Boundary Inductive Limit Local Cohomology Canonical Morphism Natural Morphism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [An1]
    Andronikof, E., Microlocalisation tempérée des distributions et des fonctions holomorphes I, CR. Acad. Sci. 303 (1986), 347–350; II 304 (1987), 511-514; See also Thèse d’Etat, Paris-Nord (juin 1987).MathSciNetMATHGoogle Scholar
  2. [An2]
    Andronikof, E., Microlocalisation tempérée, Mémoire 57 (1994), Supl. au Bull. de la Soc. Math. France 122 (2).Google Scholar
  3. [K-K]
    Kashiwara M. and T. Kawai, On the Boundary Value Problems for Elliptic Systems of Linear Differential Equations I, Proc. Japan Academy 48 (1972), 712–715; II 49 (1973), 164-168.MathSciNetMATHCrossRefGoogle Scholar
  4. [K-S1]
    Kashiwara, M. and P. Schapira, Microhyperbolic Systems, Acta Math. 142 (1974), 1–55.MathSciNetCrossRefGoogle Scholar
  5. [K-S2]
    Kashiwara, M. and P. Schapira, Microlocal Study of Sheaves, Astérisque 128 (1985); Sheaves on Manifolds, Grndlehren der Math. 292, Springer-Verlag, 1994.Google Scholar
  6. [U]
    Uchida, M., A Generalization of Bochner’s Tube Theorem for Elliptic Boundary Value Problems, RIMS Kôkyûroku, Kyoto Univ. 845, 1993, pp. 129–138.MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Tokyo 1997

Authors and Affiliations

  • Emmanuel Andronikof
    • 1
  • Nobuyuki Tose
    • 1
  1. 1.Mathematics, Hiyoshi CampusKeio UniversityHiyoshi, Yokohama, Kanagawa 223Japan

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