Prolongations of linear partial differential equations. I. A conjecture of Élie Cartan
Goldschmidt, Hubert
Annales scientifiques de l'École Normale Supérieure, Tome 1 (1968), p. 417-444 / Harvested from Numdam
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@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},
     volume = {1},
     year = {1968},
     pages = {417-444},
     doi = {10.24033/asens.1168},
     mrnumber = {38 \#3888},
     zbl = {0167.09402},
     language = {en},
     url = {http://dml.mathdoc.fr/item/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, Tome 1 (1968) pp. 417-444. doi : 10.24033/asens.1168. http://gdmltest.u-ga.fr/item/ASENS_1968_4_1_3_417_0/

[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 7,520d | Zbl 0063.00734

[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 32 #4709 | Zbl 0178.11302

[5] H. Goldschmidt, Existence theorems for analytic linear partial differential equations (Ann. Math., vol. 86, 1967, p. 246-270). | MR 36 #2933 | Zbl 0154.35103

[6] H. Goldschmidt, Integrability criteria for systems of non linear partial differential equations (J. of Differential Geometry, vol. 1, 1967, p. 269-307). | MR 37 #1746 | Zbl 0159.14101

[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 0236.14003

[8] M. Kuranishi, On É. Cartan's prolongation theorem of exterior differential systems (Amer. J. Math., vol. 79, 1957, p. 1-47). | MR 18,474d | Zbl 0077.29701

[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 29 #635 | Zbl 0119.07704

[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 0186.42503

[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 36 #5490 | Zbl 0172.13601

[13] D. Mumford, Lectures on curves on an algebraic surface (Ann. Math. Studies, No. 59, Princeton University Press, Princeton, 1966). | MR 35 #187 | Zbl 0187.42701

[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 27 #6287b | Zbl 0124.38601

[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 37 #578 | Zbl 0152.29402