Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Extension theorems
for the distribution solutions
to $\mathcal{D}$-modules with regular singularities


Authors: Hiroshi Koshimizu and Kiyoshi Takeuchi
Journal: Proc. Amer. Math. Soc. 128 (2000), 1685-1690
MSC (1991): Primary 32C38
DOI: https://doi.org/10.1090/S0002-9939-99-05494-5
Published electronically: October 27, 1999
MathSciNet review: 1695127
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Some extension theorems for the distribution solutions to $\mathcal{D}$- modules will be given. We will use the notion of regular singularities introduced by Kashiwara-Oshima (1977).


References [Enhancements On Off] (What's this?)

  • 1. E. Andronikof, Microlocalisation tempérée, Mém. Soc. Math. France, 57 (1994). MR 95e:58168
  • 2. J.M. Bony, Propagation des singularités microlocale analytique des distributions, Astérisque, 34-35 (1976), 43-91. MR 58:23199
  • 3. V. Colin, Thése at Paris VI, and a note to appear, (1997).
  • 4. A. D'Agnolo and F. Tonin, Cauchy problem for hyperbolic $\mathcal{D}$-modules with regular singularities, Pacific Journal of Mathematics, 184 (1998), 1-22. CMP 98:13
  • 5. M. Kashiwara, Algebraic study of systems of linear differential equations (Master Thesis, Tokyo Univ., 1970), Mém. Soc. Math. France, 63 (1995). MR 97f:32012
  • 6. M. Kashiwara, The Riemann-Hilbert problem for holonomic systems, Publ. Res. Inst. Math. Sci., 20 (1984), 319-365. MR 86j:58142
  • 7. M. Kashiwara and T. Oshima, Systems of differential equations with regular singularities and their boundary value problems, Ann. Math., 106 (1977), 145-200. MR 58:2914
  • 8. M. Kashiwara and P. Schapira, Micro-hyperbolic systems, Acta Math., 142 (1979), 1-55. MR 80b:58060
  • 9. M. Kashiwara and P. Schapira, Sheaves on manifolds, Grundlehlen der Math. Wiss., 292, Springer-Verlag (1990). MR 92a:58132
  • 10. T. Kawai, Extension of solutions of systems of linear differential equations, Publ. Res. Inst. Math. Sci., 12 (1976-77), 215-227. MR 54:3767
  • 11. M. Sato, T. Kawai and M. Kashiwara, Hyperfunctions and pseudodifferential equations, L.N. in Math., Springer-Verlag, 287 (1973), 265-529.
  • 12. K. Takeuchi, Edge-of-the-wedge type theorems for hyperfunction solutions, Duke Math. J., 89 (1997), 109-132. MR 98h:32015
  • 13. K. Takeuchi, Microlocal inverse image and bimicrolocalization, Publ. Res. Inst. Math. Sci., 34 (1998), 135-153. MR 99f:32018

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 32C38

Retrieve articles in all journals with MSC (1991): 32C38


Additional Information

Hiroshi Koshimizu
Affiliation: Department of Mathematical Sciences, University of Tokyo, 3-8-1, Komaba, Meguro-ku, 153, Japan

Kiyoshi Takeuchi
Affiliation: Department of Mathematics, Hiroshima University, 1-3-1, Kagamiyama, Higashi-hiroshima, Hiroshima, 739-8526, Japan
Email: takeuchi@top2.math.sci.hiroshima-u.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-99-05494-5
Keywords: Distribution, boundary value problem
Received by editor(s): July 10, 1998
Published electronically: October 27, 1999
Dedicated: Dedicated to the Memory of Our Friend, E. Andronikof
Communicated by: Lesley M. Sibner
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society