Algebraic study of systems of partial differential equations

Masaki Kashiwara

Mémoires de la Société Mathématique de France (1995)

  • Volume: 63, page I1-XIV72
  • ISSN: 0249-633X

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Kashiwara, Masaki. "Algebraic study of systems of partial differential equations." Mémoires de la Société Mathématique de France 63 (1995): I1-XIV72. <http://eudml.org/doc/94915>.

@article{Kashiwara1995,
author = {Kashiwara, Masaki},
journal = {Mémoires de la Société Mathématique de France},
keywords = {M. Kashiwara's thesis; -modules},
language = {eng},
pages = {I1-XIV72},
publisher = {Société mathématique de France},
title = {Algebraic study of systems of partial differential equations},
url = {http://eudml.org/doc/94915},
volume = {63},
year = {1995},
}

TY - JOUR
AU - Kashiwara, Masaki
TI - Algebraic study of systems of partial differential equations
JO - Mémoires de la Société Mathématique de France
PY - 1995
PB - Société mathématique de France
VL - 63
SP - I1
EP - XIV72
LA - eng
KW - M. Kashiwara's thesis; -modules
UR - http://eudml.org/doc/94915
ER -

References

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  2. [2] E. Cartan, Les systèmes différentiels extérieurs et leurs applications géométriques, Hermann, 1945. Zbl0063.00734MR7,520d
  3. [3] H. Cartan and S. Eilenberg, Homological Algebra, Princeton University Press, 1956. Zbl0075.24305MR17,1040e
  4. [4] J. Dieudonné and A. Grothendieck, Eléments de géométrie algébrique, Chapitre II, III, IV, Inst. Hautes Etudes Sci. Publ. Math. 8, 11, 17, 20, 24, 32. Zbl0136.15901
  5. [5] J. Frisch, Points de platitude d'un morphisme d'espaces analytiques complexes, Invent. Math. 4 (1967), 118-138. Zbl0167.06803MR36 #5388
  6. [6] R. Hartshorne, Residues and duality, Lecture Notes in Mathematics 20, Springer, 1966. Zbl0212.26101MR36 #5145
  7. [7] R. Harvey and R. O. Wells Jr., Compact holomorphically convex subsets of a Stein manifold, Trans. Amer. Math. Soc. 136 (1969), 509-516. Zbl0175.37204MR38 #3470
  8. [8] H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero. I, II, Ann. of Math. 79 (1964), 109-326. Zbl0122.38603MR33 #7333
  9. [9] C. Houzel, Géométrie analytique locale, Séminaire Henri Cartan, 13ème année : 1960/1961, Ecole Normale Supérieure, 1962. Zbl0121.15906
  10. [10] * M. Kashiwara and T. Kawai, Pseudo-differential operators in the theory of hyperfunctions, Proc. Japan Acad. 46 (1970), 1130-1134. Zbl0229.47034MR47 #4295
  11. [11] B. Malgrange, Cohomologie de Spencer (d'après Quillen). 
  12. [12] V. P. Palamodov, Differential operators in the class of convergent power series, and the Weierstrass preparation theorem, Funkcional. Anal. i Prilozen 2 (1968), 58-69. Zbl0176.45701MR38 #4795
  13. [13] V. P. Palamodov, Linear differential operators with constant coefficients, Grundlehren der mathematischen Wissenschaften 168, Springer, 1970. Zbl0191.43401MR41 #8793
  14. [14] D. Quillen, Formal properties of overdetermined system of linear partial differential equations, Thesis (1964). Zbl1295.35005
  15. [15] M. Sato, Theory of hyperfunctions I, II, Journ. Fac. Sci. Univ. Tokyo Sect. I 8 (1959), 139-193; ibid. 8 (1960), 387-437. Zbl0087.31402MR24 #A2237
  16. [16] M. Sato, Hyperfunctions and partial differential equations, Proceedings of the International Conference on Functional Analysis and Related Topics (Tokyo, April, 1969), University of Tokyo Press, Tokyo, 1970. Zbl0208.35801
  17. [17] * T. Kawai and H. Komatsu, Boundary values of hyperfunction solutions of linear partial differential equations, Publ. Res. Inst. Math. Sci. 7 (1971/1972), 95-104. Zbl0225.35032

Citations in EuDML Documents

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  1. Jean-François Pommaret, Alban Quadrat, A functorial approach to the behaviour of multidimensional control systems
  2. Ana Rita Martins, Temperate holomorphic solutions and regularity of holonomic D-modules on curves
  3. Corrado Marastoni, Grassmann duality for 𝒟 -modules
  4. John Coates, Iwasawa algebras and arithmetic
  5. Anne Virrion, Dualité locale et holonomie pour les 𝒟 -modules arithmétiques
  6. Waichiro Matsumoto, The Cauchy problem for systems through the normal form of systems and theory of weighted determinant
  7. Pierre Berthelot, 𝒟 -modules arithmétiques. II: Descente par Frobenius
  8. François Loeser, Exposants p -adiques et théorèmes d’indice pour les équations différentielles p -adiques
  9. Alban Quadrat, An introduction to constructive algebraic analysis and its applications
  10. Claude Sabbah, Classes caractéristiques et théorèmes d'indice : point de vue microlocal

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