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Complexes of differential operators. The Mayer-Vietoris sequence. (English) Zbl 0332.58016


MSC:

58J99 Partial differential equations on manifolds; differential operators
35N15 \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs
58J10 Differential complexes
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References:

[1] Andreotti, A.: Complexes of differential operators. Yale Mathematical Monographs 6 (1975) · Zbl 0309.58020
[2] Andreotti, A., Hill, C.D.: E.E. Levi convexity and the Hans Lewy problem. Part I: Reduction to vanishing theorems. Ann. Scuola Norm. Sup. Pisa26, 325–363 (1972) · Zbl 0256.32007
[3] Andreotti, A., Hill, C. D.: E.E. Levi convexity and the Hans Lewy problem. Part II: Vanishing theorems. Ann. Scuola Norm. Sup. Pisa26, 747–806 (1972) · Zbl 0283.32013
[4] Andreotti, A., Hill, C. D., Łojasiewicz, S., MacKichan, B.: Mayer-Vietories sequences for complexes of differential operators. To appear in Bull. Amer. Math. Soc. · Zbl 0325.58018
[5] Andreotti, A., Kas, A.: Duality on complex spaces. Ann. Scuola Norm. Sup. Pisa27, 187–263 (1973) · Zbl 0278.32007
[6] Bourbaki, N.: Topologie générale, Ch. l, Structures topologiques, 4e edition. Paris: Hermann 1965
[7] Guillemin, V.: Some algebraic results concerning the characteristics of overdetermined partial differential equations. Amer. J. Math.90, 270–284 (1968) · Zbl 0162.40601
[8] Harvey, C., Harvey, F. R.: Open mappings and the lack of fully completeness ofD’({\(\Omega\)}). Proc. Amer. Math. Soc.25, 786–790 (1970) · Zbl 0197.39101
[9] Hill, C. D., MacKichan, B.: Hyperfunction cohomology classes and their boundary values. To appear · Zbl 0367.46037
[10] Kuranishi, M.: On the complexes on the boundary induced by elliptic complexes of differential operators, in Contributions to Analysis. New York-London: Academic Press (1974) · Zbl 0293.58012
[11] MacKichan, B.: A generalization to overdetermined systems of the notion of diagonal operators. II: Hyperbolic operators. Acta Math.134, 239–274 (1975) · Zbl 0313.35059
[12] MacKichan, B.: The Cauchy problem for overdetermined systems of partial differential equations. Proc. of the Rencontre sur l’Analyse Complexe à Plusieurs Variables et les Systemes Surdéterminés, 1974. Montréal: Les Presses de l’Université de Montréal 1975
[13] Polking, J., Wells, R.: Boundary values of Dolbeault cohomology classes and a generalized Bochner-Hartogs theorem. To appear · Zbl 0379.32019
[14] Rham, G. de: Variétés différentiables. Paris: Hermann 1955
[15] Rockland, C.: A new construction of the Guillemin Poincaré complex. Princeton thesis (1972)
[16] Serre, J.-P.: Un théorème de dualité. Comm. Math. Helvetici29, 9–26 (1955) · Zbl 0067.16101
[17] Spencer, D. C.: Overdetermined systems of linear partial differential equations. Bull. Amer. Math. Soc.75, 179–239 (1969) · Zbl 0185.33801
[18] Störmark, O.: A note on a paper by Andreotti-Hill concerning the Hans Lewy problem. To appear in Ann. Scuola Norm. Sup. Pisa
[19] Trèves, F.: Topological Vector Spaces, Distributions, and Kernels. New York-London: Academic Press 1967 · Zbl 0171.10402
[20] Whitney, H.: Analytic extensions of differentiable functions defined in closed sets. Trans. Amer. Math. Soc.36, 63–89 (1934) · Zbl 0008.24902
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