×

zbMATH — the first resource for mathematics

Prolongations of linear partial differential equations. I: A conjecture of Elie Cartan. (English) Zbl 0167.09402

PDF BibTeX XML Cite
Full Text: DOI Numdam EuDML
References:
[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 . · Zbl 0136.03404
[3] É. CARTAN , Les systèmes différentiels extérieurs et leurs applications géométriques , Hermann, Paris, 1945 . MR 7,520d | Zbl 0063.00734 · Zbl 0063.00734
[4] L. EHRENPREIS , V. W. GUILLEMIN and S. STERNBERG , On Spencer’s estimate for \delta -Poincaré (Ann. Math., vol. 82, 1965 , p. 128-138). MR 32 #4709 | Zbl 0178.11302 · Zbl 0178.11302 · doi:10.2307/1970565
[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 · Zbl 0154.35103 · doi:10.2307/1970689
[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 · 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 · Zbl 0236.14003 · numdam:SB_1960-1961__6__249_0 · eudml:109614
[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 · Zbl 0077.29701 · doi:10.2307/2372381
[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 · Zbl 0119.07704 · doi:10.2307/2373171
[10] B. MALGRANGE , Cohomologie de Spencer (d’après QUILLEN), Séminaire mathématique, Orsay, 1966 . Article · minidml.mathdoc.fr
[11] B. MALGRANGE , Théorie analytique des équations différentielles , Séminaire Bourbaki, No. 329, 1966 - 1967 . Numdam | Zbl 0186.42503 · Zbl 0186.42503 · numdam:SB_1966-1968__10__261_0 · eudml:109730
[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 · Zbl 0172.13601 · doi:10.2977/prims/1195195656
[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 · Zbl 0187.42701
[14] D. G. QUILLEN , Formal properties of over-determined systems of linear partial differential equations (Ph. D. thesis, Harvard University, 1964 ). · Zbl 1295.35005
[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 · Zbl 0124.38601 · doi:10.2307/1970277
[16] S. STERNBERG , Notes on partial differential equations , Mimeographed notes, Harvard University (to appear). · Zbl 0206.39102
[17] W. J. SWEENEY , The \delta -Poincaré estimate (Pac. J. Math., vol. 20, 1967 , p. 559-570). Article | MR 37 #578 | Zbl 0152.29402 · Zbl 0152.29402 · doi:10.2140/pjm.1967.20.559 · minidml.mathdoc.fr
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.