Advertisement

Second-microlocalization and asymptotic expansions

  • Masaki Kashiwara
  • Takahiro Kawai
Part I Microfunctions, Microlocal Calculus and Related Topics
Part of the Lecture Notes in Physics book series (LNP, volume 126)

Abstract

The asymptotic expansions of (holonomic) microfunctions is neatly dealt with by the second micro-localization.

Keywords

Asymptotic Expansion Compact Subset Holomorphic Function Lagrangian Submanifold Symbol Sequence 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Barbasch, D. and D. A. Vogan: The local structure of characters. To appear.Google Scholar
  2. [2]
    Boutet de Monvel, L. and P. Krée: Pseudo-differential operators and Gevrey classes. Ann. Inst. Fourier, Grenoble, 17, 295–323 (1967).Google Scholar
  3. [3]
    Hörmander, L.: Fourier integral operators. I. Acta Math., 127 79–183 (1971)Google Scholar
  4. [4]
    Iagolnitzer, D. and H. P. Stapp: The pole-factorization theorem in S-matrix theory. Commun. math. Phys., 57, 1–30 (1977).CrossRefGoogle Scholar
  5. [5]
    Jeanquartier, P.: Développement asymptotique de la distribution de Dirac attachée à une fonction analytique. C. R. Acad. Sci. Paris, Série A, 271, 1159–1161 (1970).Google Scholar
  6. [6]
    Kashiwara, M.: On the holonomic systems of linear differential equations. II. Inverntiones math., 49, 121–135 (1978).CrossRefGoogle Scholar
  7. [7]
    Kashiwara, M. and T. Kawai: Tficro-hyperbolic pseudo-differential operators I. J. Math. Soc. Japan, 27, 359–404 (1975).Google Scholar
  8. [8]
    —: On holonomic systems of micro-differential equations. III — Systems with regular singularities—. To appear. (RIMS preprint No.293.)Google Scholar
  9. [9]
    —: The theory of holonomic systems with regular singularities and its relevance to physical problems. This proceedings.Google Scholar
  10. [10]
    Kashiwara, M. and Y. Laurent: Théorèmes d'annulation et double microlocalisation. To appear.Google Scholar
  11. [11]
    Kashiwara, M. and T. Oshima: Systems of differential equations with regular singularities and their boundary value problems. Ann. of Math., 106, 145–200 (1977).Google Scholar
  12. [12]
    Kashiwara, M. and P. Schapira: Micro-hyperbolic systems. Acta Math., 142, 1–55 (1979).Google Scholar
  13. [13]
    Kawai, T. and H. P. Stapp: Discontinuity formula and Sato's conjecture. Publ. RIMS, Kyoto Univ., 12 Suppl., 155–232 (1977).Google Scholar
  14. [14]
    Laurent, Y.: Double microlocalisation et problème de Cauchy dans le domaine complex. Proc. of the conference at St. Cast, 1979.Google Scholar
  15. [15]
    —: The report in this proceedings.Google Scholar
  16. [16]
    Monteiro-Fernandes, T.: Thèse de 3ème cycle à l'Université, Paris-Nord (1978).Google Scholar
  17. [17]
    Sato, M., T. Kawai and M. Kashiwara (referred to as S-K-K [17]): Microfunctions and pseudo-differential equations. Lecture Notes in Math. No.287, pp. 265–529, Berlin-Heidelberg-New York: Springer, 1973.Google Scholar
  18. [18]
    Tahara, H.: Fuchsian type equations and Fuchsian hyperbolic equations. To appear in Japanese J. Math. *** DIRECT SUPPORT *** A3418084 00002Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Masaki Kashiwara
    • 1
    • 2
  • Takahiro Kawai
    • 3
  1. 1.Départment de MathématiquesUniversité de Paris-SudOrsayFrance
  2. 2.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan
  3. 3.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan

Personalised recommendations