Prolongations of linear partial differential equations. I. A conjecture of Élie Cartan
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 1 (1968) no. 3, pp. 417-444.
@article{ASENS_1968_4_1_3_417_0,
     author = {Goldschmidt, Hubert},
     title = {Prolongations of linear partial differential equations. {I.} {A} conjecture of {\'Elie} {Cartan}},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {417--444},
     publisher = {Elsevier},
     volume = {Ser. 4, 1},
     number = {3},
     year = {1968},
     doi = {10.24033/asens.1168},
     zbl = {0167.09402},
     mrnumber = {38 #3888},
     language = {en},
     url = {http://www.numdam.org/articles/10.24033/asens.1168/}
}
TY  - JOUR
AU  - Goldschmidt, Hubert
TI  - Prolongations of linear partial differential equations. I. A conjecture of Élie Cartan
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 1968
DA  - 1968///
SP  - 417
EP  - 444
VL  - Ser. 4, 1
IS  - 3
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.24033/asens.1168/
UR  - https://zbmath.org/?q=an%3A0167.09402
UR  - https://www.ams.org/mathscinet-getitem?mr=38 #3888
UR  - https://doi.org/10.24033/asens.1168
DO  - 10.24033/asens.1168
LA  - en
ID  - ASENS_1968_4_1_3_417_0
ER  - 
%0 Journal Article
%A Goldschmidt, Hubert
%T Prolongations of linear partial differential equations. I. A conjecture of Élie Cartan
%J Annales scientifiques de l'École Normale Supérieure
%D 1968
%P 417-444
%V Ser. 4, 1
%N 3
%I Elsevier
%U https://doi.org/10.24033/asens.1168
%R 10.24033/asens.1168
%G en
%F ASENS_1968_4_1_3_417_0
Goldschmidt, Hubert. Prolongations of linear partial differential equations. I. A conjecture of Élie Cartan. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 1 (1968) no. 3, pp. 417-444. doi : 10.24033/asens.1168. http://www.numdam.org/articles/10.24033/asens.1168/

[1] R. Bott, Notes on the Spencer resolution, Mimeographed notes, Harvard University, 1963.

[2] N. Bourbaki, Éléments de mathématique, Topologie générale ; Chapitre 2 : Structures uniformes, 4e édition, Hermann, Paris, 1965.

[3] É. Cartan, Les systèmes différentiels extérieurs et leurs applications géométriques, Hermann, Paris, 1945. | MR | Zbl

[4] L. Ehrenpreis, V. W. Guillemin and S. Sternberg, On Spencer's estimate for δ-Poincaré (Ann. Math., vol. 82, 1965, p. 128-138). | MR | Zbl

[5] H. Goldschmidt, Existence theorems for analytic linear partial differential equations (Ann. Math., vol. 86, 1967, p. 246-270). | MR | Zbl

[6] H. Goldschmidt, Integrability criteria for systems of non linear partial differential equations (J. of Differential Geometry, vol. 1, 1967, p. 269-307). | MR | Zbl

[7] A. Grothendieck, Techniques de construction et théorèmes d'existence en géométrie algébrique ; IV : Les schémas de Hilbert, Séminaire Bourbaki, No. 221, 1960-1961. | Numdam | Zbl

[8] M. Kuranishi, On É. Cartan's prolongation theorem of exterior differential systems (Amer. J. Math., vol. 79, 1957, p. 1-47). | MR | Zbl

[9] M. Kuranishi, Sheaves defined by differential equations and application to deformation theory of pseudo-group structures (Amer. J. Math., vol. 86, 1964, p. 379-391). | MR | Zbl

[10] B. Malgrange, Cohomologie de Spencer (d'après QUILLEN), Séminaire mathématique, Orsay, 1966.

[11] B. Malgrange, Théorie analytique des équations différentielles, Séminaire Bourbaki, No. 329, 1966-1967. | Numdam | Zbl

[12] M. Matsuda, Cartan-Kuranishi's prolongation of differential systems combined with that of Lagrange and Jacobi (Pub. Res. Inst. Math. Sci., Ser. A, vol. 3, 1967, p. 69-84). | MR | Zbl

[13] D. Mumford, Lectures on curves on an algebraic surface (Ann. Math. Studies, No. 59, Princeton University Press, Princeton, 1966). | MR | Zbl

[14] D. G. Quillen, Formal properties of over-determined systems of linear partial differential equations (Ph. D. thesis, Harvard University, 1964).

[15] D. C. Spencer, Deformation of structures on manifolds defined by transitive, continuous pseudogroups : I, II (Ann. Math., vol. 76, 1962, p. 306-445). | MR | Zbl

[16] S. Sternberg, Notes on partial differential equations, Mimeographed notes, Harvard University (to appear).

[17] W. J. Sweeney, The δ-Poincaré estimate (Pac. J. Math., vol. 20, 1967, p. 559-570). | MR | Zbl

Cited by Sources: