On the absence of Poincaré lemma in tangential Cauchy-Riemann complexes

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1. [0] A. Andreotti, Nine lectures in complex analysis, C.I.M.E.1973, Cremonese, Roma, 1974. Zbl0353.32021MR442262
2. [1] A. Andreotti, Complexes of partial differential operators, Yale Univ. Press, 1975. Zbl0309.58020MR413192
3. [2] A. Andreotti - C.D. Hill, Complex characteristic coordinates and tangential Cauchy-Riemann equations, Ann. Scuola Norm. Sup. Pisa, 26 (1972), pp. 299-324. Zbl0256.32006MR460724
4. [3] A. Andreotti - C.D. Hill, E. E. Levi convexity and the Hans Lewy problem, Part I and II, Ann. Scuola Norm. Sup. Pisa, 26 (1972), pp. 325-363 and pp. 747-806. Zbl0283.32013
5. [4] A. Andreotti - M. Nacinovich, On analytic and C∞ Poincaré lemma, to appear in « Advances in Math. ». Zbl0471.58021
6. [5] L. Boutet De Monvel, Hypoelliptic operators with double characteristics and related pseudodifferential operators, Comm. Pure Appl. Math., 27 (1974), pp. 585-639. Zbl0294.35020MR370271
7. [6] R. Godement, Theorie des faisceaux, Hermann, Paris, 1958. Zbl0080.16201MR102797
8. [7] L. Hörmander, Linear Partial Differential Operators, Springer, Berlin, G. Hingen, Heidelberg, 1963. Zbl0108.09301MR161012
9. [8] J.J. Kohn, Boundaries of complex manifolds. Proceedings Conference on Complex Analysis, Springer, Berlin, Heidelberg, New York, 1965, pp. 81-94. Zbl0166.36003MR175149
10. [9] H. Lewy, An example of a smooth partial differential equation without solutions, Ann. of Math., 66 (1957), pp. 155-158. Zbl0078.08104MR88629
11. [10] S. Łojasiewicz, Sur le problème de la division, Studia Math., 8 (1959), pp. 87-136. Zbl0115.10203
12. [11] B. Malgrange, Ideals of differentiable functions, Oxford Univ. Press, 1966. Zbl0177.17902MR212575
13. [12] V.P. Maslov, Operational methods, Mir publisher, Moscow, 1973. Zbl0449.47002MR512495
14. [13] I. Naruki, Localization principle for differential complexes and its applications, R.I.M.S. 94, Kyoto (1971). Zbl0246.35072MR321143
15. [14] H.K. Nickfrson, On the complex form of the Poincaré lemma, Proc. Amer. Math. Soc., 9 (1958), pp. 183-188. Zbl0091.36701MR95975
16. [15] M. Sato - T. Kawai - N. Kashiwara, Microfunctions and pseudodifferential equations, Lecture Notes in Math. n. 287, pp. 265-529, SpringerBerlin, Heidelberg, New York, 1973. Zbl0277.46039MR420735
17. [16] A. Sommerfeld, Partial differential equations in physics, Academic Press-New York, 1967. Zbl0034.35702MR29463
18. [17] F. Treves, Study of a model in the theory of complexes of pseudodifferential operators, Ann. of Math. (2), 104 (1976), pp. 269-324. Zbl0354.35067MR426068

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