Elliptic boundary value problems in the space of distributions

  • Emmanuel Andronikof
  • Nobuyuki Tose


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]).


Elliptic Boundary Inductive Limit Local Cohomology Canonical Morphism Natural Morphism 
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  1. [An1]
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  2. [An2]
    Andronikof, E., Microlocalisation tempérée, Mémoire 57 (1994), Supl. au Bull. de la Soc. Math. France 122 (2).Google Scholar
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    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
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    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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