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Overdetermined systems of linear partial differential equations. (English) Zbl 0185.33801

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[1] R. Bott, Notes on the Spencer resolution, Harvard University, Cambridge, Mass., 1963.
[2] C. Buttin, Existence of a homotopy operator for Spencer’s sequence in the analytic case, Pacific J. Math. 21 (1967), 219 – 240. · Zbl 0148.36102
[3] H. Cartan, Familles d’espaces complexes et fondements de la géométrie analytique, Séminaire Henri Cartan, 1961/62, Secrétariat Mathématique, Paris, 1963.
[4] Bohumil Cenkl, Vanishing theorem for an elliptic differential operator, J. Differential Geometry 1 (1967), 381 – 418. · Zbl 0162.42403
[5] Leon Ehrenpreis, Victor W. Guillemin, and Shlomo Sternberg, On Spencer’s estimate for \?-Poincaré, Ann. of Math. (2) 82 (1965), 128 – 138. · Zbl 0178.11302 · doi:10.2307/1970565 · doi.org
[6] Hubert Goldschmidt, Existence theorems for analytic linear partial differential equations, Ann. of Math. (2) 86 (1967), 246 – 270. · Zbl 0154.35103 · doi:10.2307/1970689 · doi.org
[7] Hubert Goldschmidt, Integrability criteria for systems of nonlinear partial differential equations, J. Differential Geometry 1 (1967), 269 – 307. · Zbl 0159.14101
[8] Hubert Goldschmidt, Prolongations of linear partial differential equations. I. A conjecture of Élie Cartan, Ann. Sci. École Norm. Sup. (4) 1 (1968), 417 – 444. · Zbl 0167.09402
[9] Hubert Goldschmidt, Prolongations of linear partial differential equations. II. Inhomogeneous equations, Ann. Sci. École Norm. Sup. (4) 1 (1968), 617 – 625. · Zbl 0172.13602
[10] H. Goldschmidt, (e) Estimates for analytic partial differential equations (to appear). · Zbl 0154.35103
[11] A. Grothendieck, Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schémas. II, Inst. Hautes Études Sci. Publ. Math. 24 (1965), 231 (French). · Zbl 0135.39701
[12] Victor Guillemin, Some algebraic results concerning the characteristics of overdetermined partial differential equations, Amer. J. Math. 90 (1968), 270 – 284. · Zbl 0162.40601 · doi:10.2307/2373436 · doi.org
[13] Victor Guillemin and Masatake Kuranishi, Some algebraic results concerning involutive subspaces, Amer. J. Math. 90 (1968), 1307 – 1320. · Zbl 0186.16403 · doi:10.2307/2373301 · doi.org
[14] V. Guillemin, D. Quillen, and S. Sternberg, The classification of the complex primitive infinite pseudogroups, Proc. Nat. Acad. Sci. U.S.A. 55 (1966), 687 – 690. · Zbl 0192.12702
[15] Lars Hörmander, Linear partial differential operators, Third revised printing. Die Grundlehren der mathematischen Wissenschaften, Band 116, Springer-Verlag New York Inc., New York, 1969. · Zbl 0175.39201
[16] Lars Hörmander, Pseudo-differential operators, Comm. Pure Appl. Math. 18 (1965), 501 – 517. · Zbl 0125.33401 · doi:10.1002/cpa.3160180307 · doi.org
[17] Lars Hörmander, Pseudo-differential operators and non-elliptic boundary problems, Ann. of Math. (2) 83 (1966), 129 – 209. · Zbl 0132.07402 · doi:10.2307/1970473 · doi.org
[18] J. J. Kohn, Harmonic integrals on strongly pseudo-convex manifolds. I, Ann. of Math. (2) 78 (1963), 112 – 148. · Zbl 0161.09302 · doi:10.2307/1970506 · doi.org
[19] J. J. Kohn, Harmonic integrals on strongly pseudo-convex manifolds. II, Ann. of Math. (2) 79 (1964), 450 – 472. · Zbl 0178.11305 · doi:10.2307/1970404 · doi.org
[20] J. J. Kohn, Boundaries of complex manifolds, Proc. Conf. Complex Analysis (Minneapolis, 1964) Springer, Berlin, 1965, pp. 81 – 94.
[21] J. J. Kohn and L. Nirenberg, Non-coercive boundary value problems, Comm. Pure Appl. Math. 18 (1965), 443 – 492. · Zbl 0125.33302 · doi:10.1002/cpa.3160180305 · doi.org
[22] J. J. Kohn and L. Nirenberg, An algebra of pseudo-differential operators, Comm. Pure Appl. Math. 18 (1965), 269 – 305. · Zbl 0171.35101 · doi:10.1002/cpa.3160180121 · doi.org
[23] Masatake Kuranishi, On E. Cartan’s prolongation theorem of exterior differential systems, Amer. J. Math. 79 (1957), 1 – 47. · Zbl 0077.29701 · doi:10.2307/2372381 · doi.org
[24] Masatake Kuranishi, Sheaves defined by differential equations and application to deformation theory of pseudo-group structures, Amer. J. Math. 86 (1964), 379 – 391. · Zbl 0119.07704 · doi:10.2307/2373171 · doi.org
[25] Hans Lewy, An example of a smooth linear partial differential equation without solution, Ann. of Math. (2) 66 (1957), 155 – 158. · Zbl 0078.08104 · doi:10.2307/1970121 · doi.org
[26] B. MacKichan, A generalization to overdetermined systems of the notion of diagonal operators, Thesis, Stanford University, Stanford, Calif., 1968 (to appear). · Zbl 0263.35077
[27] B. Malgrange, (a) Cohomologie de Spencer (d’après Quillen), Secrétariat Mathématique d’Orsay, 1966.
[28] Bernard Malgrange, Théorie analytique des équations différentielles, Séminaire Bourbaki, Vol. 10, Soc. Math. France, Paris, 1995, pp. Exp. No. 329, 261 – 273 (French).
[29] Charles B. Morrey Jr., The analytic embedding of abstract real-analytic manifolds, Ann. of Math. (2) 68 (1958), 159 – 201. · Zbl 0090.38401 · doi:10.2307/1970048 · doi.org
[30] C. B. Morrey Jr., The \partial -Neumann problem on strongly pseudo-convex manifolds, Outlines Joint Sympos. Partial Differential Equations (Novosibirsk, 1963), Acad. Sci. USSR Siberian Branch, Moscow, 1963, pp. 171 – 178.
[31] D. G. Quillen, Formal properties of over-determined systems of linear partial differential equations, Thesis, Harvard University, Cambridge, Mass., 1964 (unpublished).
[32] Jean-Pierre Serre, Faisceaux algébriques cohérents, Ann. of Math. (2) 61 (1955), 197 – 278 (French). · Zbl 0067.16201 · doi:10.2307/1969915 · doi.org
[33] D. C. Spencer, Deformation of structures on manifolds defined by transitive, continuous pseudogroups. I. Infinitesimal deformations of structure, Ann. of Math. (2) 76 (1962), 306 – 398. , https://doi.org/10.2307/1970277 D. C. Spencer, Deformation of structures on manifolds defined by transitive, continuous pseudogroups. II. Deformations of structure, Ann. of Math. (2) 76 (1962), 399 – 445. · Zbl 0124.38601 · doi:10.2307/1970367 · doi.org
[34] D. C. Spencer, Deformation of structures on manifolds defined by transitive, continuous pseudogroups. III. Structures defined by elliptic pseudogroups, Ann. of Math. (2) 81 (1965), 389 – 450. · Zbl 0192.29603 · doi:10.2307/1970623 · doi.org
[35] D. C. Spencer, A type of formal exterior differentiation associated with pseudogroups, Scripta Math. 26 (1963), 101 – 106 (1963). · Zbl 0112.14603
[36] S. Sternberg, Partial differential equations, Lectures at the University of Pennsylvania, January-February, 1967 (polycopied).
[37] W. J. Sweeney, ”The \?-Poincaré estimate”, Pacific J. Math. 20 (1967), 559 – 570. · Zbl 0152.29402
[38] William J. Sweeney, The \?-Neumann problem, Acta Math. 120 (1968), 223 – 277. · Zbl 0159.38402 · doi:10.1007/BF02394611 · doi.org
[39] W. J. Sweeney, A noncompact Dirichlet norm, Proc. Nat. Acad. Sci. U.S.A. 58 (1967), 2193 – 2195. · Zbl 0171.35003
[40] Ngô van Quê, Du prolongement des espaces fibrés et des structures infinitésimales, Ann. Inst. Fourier (Grenoble) 17 (1967), no. fasc. 1, 157 – 223 (French). · Zbl 0157.28506
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