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Literature Cited
R. O. Wells, Jr., Differential Analysis on Complex Manifolds, Prentice-Hall, Englewood Cliffs (1973).
F. John, Plane Waves and Spherical Means Applied to Partial Differential Equations, Wiley-Interscience, New York (1955).
R. Harvey and J. Polking, “Fundamental solutions in complex analysis. Part 1. The Cauchy-Riemann operator,” Duke Math. J.,46, No. 2, 253–300 (1979).
R. Harvey and J. Polking, “Fundamental solutions in complex analysis. Part II. The induced Cauchy-Riemann operator,” Duke Math. J.,46, No. 2, 301–340 (1979).
N. Bourbaki, Variétés Différentielles et Analytiques. Fascicule de Résultats, Hermann, Paris (1971).
V. S. Vladimirov and V. V. Zharinov, “Closed forms associated with linear differential operators,” Differents. Uravn.,16, No. 5, 845–867 (1980).
W. Koppelman, “The Cauchy integral for differential forms,” Bull. Am. Math. Soc.,73, No. 4, 554–556 (1967).
F. Norguet, “Introduction aux fonctions de plusieurs variables complexes. Représentation intégrales,” Lect. Notes Math.,409, 1–97 (1974).
V. P. Palamodov, Linear Differential Operators with Constant Coefficients, Springer-Verlag, Berlin (1970).
N. N. Tarkhanov, “A formula and estimates for the solutions of the equation du=f in a domain and on the boundary of the domain,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 5, 58–66 (1980).
J. J. Kohn and L. Nirenberg, “Noncoercive boundary value problems,” Commun. Pure Appl. Math.,18, 443–492 (1965).
W. J. Sweeney, “The D-Neumann problem,” Acta Math.,120, Nos. 3–4, 223–277 (1968).
A. Andreotti, “Complessi di operatori differenziali,” Boll. Un. Mat. Ital.,13A, 273–281 (1976).
D. C. Spencer, “Overdetermined systems of linear partial differential equations,” Bull. Am. Math. Soc.,75, No. 2, 179–239 (1969).
J. J. Kohn, “Harmonic integrals on strongly pseudoconvex manifolds. I,” Ann. Math.,78, 112–148 (1963).
J. J. Kohn, “Harmonic integrals on strongly pseudoconvex manifolds. II,” Ann. Math.,79, 450–472 (1964).
B. Cenkl, “Vanishing theorem for an elliptic differential operator,” J. Diff. Geom.,1, 381–418 (1967).
L. Hörmander, “The Frobenius-Nirenberg theorem,” Ark. Mat.,5, No. 5, 425–432 (1965).
G. M. Khenkin and E. M. Chirka, “Boundary properties of holomorphic functions of several complex variables,” Itogi Nauki i Tekhniki, Sov. Probl. Mat.,4, 13–142 (1975).
G. M. Khenkin, “H. Lewy's equation and analysis on a pseudoconvex manifold,” Usp. Mat. Nauk,32, No. 3, 57–118 (1977).
N. N. Tarkhanov, “An analogue of the logarithmic residue formula for solutions of firstorder elliptic systems, and weighted estimates for the solutions of the d-problem,” Sib. Mat. Zh.,23, No. 3, 188–197 (1982).
J. J. Kohn, “Differential complexes,” in: Proc. Int. Congr. Math. (Moscow, 1966), Mir, Moscow (1968), pp. 402–409.
A. V. Romanov, “A formula and estimates for the solutions of the tangential Cauchy-Riemann equation,” Mat. Sb.,99, No. 1, 58–83 (1976).
L. A. Aizenberg and Sh. A. Dautov, Differential Forms That Are Orthogonal to Holomorphic Functions or Forms, and Their Properties [in Russian], Nauka, Novosibirsk (1975).
J. J. Kohn and H. Rossi, “On the extension of holomorphic functions from the boundary of a complex manifold,” Ann. Math.,81, No. 3, 451–472 (1965).
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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 25, No. 4, pp. 179–191, July–August, 1984.
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Tarkhanov, N.N. A nuclear approach to solving the equation Pu=f for an elliptic complex P. Sib Math J 25, 654–665 (1984). https://doi.org/10.1007/BF00968906
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DOI: https://doi.org/10.1007/BF00968906