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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Global solvability of an abstract complex


Authors: Fernando Cardoso and Jorge Hounie
Journal: Proc. Amer. Math. Soc. 65 (1977), 117-124
MSC: Primary 35N99; Secondary 58G15
MathSciNet review: 0463721
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Abstract | References | Similar Articles | Additional Information

Abstract: In a recent paper F. Treves studied a model of complexes of pseudodifferential operators in an open set of $ {R^n}$, establishing necessary and sufficient conditions for its semiglobal solvability. In the present paper, the authors give necessary and sufficient conditions for the global solvability of an analogous complex defined on an orientable, compact smooth manifold without boundary.


References [Enhancements On Off] (What's this?)

  • [1] G. de Rham, Variétés différentiables, Actualités Sci. Indust., no. 1222 = Publ. Inst. Math. Univ. Nancago III, Hermann, Paris, 1955. MR 16, 957.
  • [2] François Treves, Study of a model in the theory of complexes of pseudodifferential operators, Ann. of Math. (2) 104 (1976), no. 2, 269–324. MR 0426068 (54 #14014)
  • [3] -, Solvability of a model in the theory of complexes of pseudodifferential operators, Lectures given by F. Treves (Recife, 1976), written by J. Hounie (to appear).

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0463721-8
PII: S 0002-9939(1977)0463721-8
Keywords: Abstract complexes, global solvability, forms, currents, compatibility conditions, de Rham cohomology
Article copyright: © Copyright 1977 American Mathematical Society