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Proceedings of the American Mathematical Society

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Pseudoholomorphic functions with nonantiholomorphic characteristics

Author: Akira Koohara
Journal: Proc. Amer. Math. Soc. 84 (1982), 217-224
MSC: Primary 32A99
MathSciNet review: 637172
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Abstract: Let $ \kappa (z) \in {C^\infty }(\Omega )$ and $ \left\Vert \kappa \right\Vert < 1$. Necessary and sufficient conditions for the system of equations $ \partial \bar f = \kappa (z)\partial f$ to be locally plentiful are given, and under them a representation of $ \kappa $ also is given.

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  • [1] L. Bers and L. Nirenberg, On a representation theorem for linear elliptic systems with discontinuous coefficients and its applications, Convegno Internazionale sulle Equazioni Lineari alle Derivate Parziali, Trieste, 1954, Edizioni Cremonese, Roma, 1955, pp. 111–140. MR 0076981
  • [2] Sin Hitotumatu, On quasi-conformal functions of several complex variables, J. Math. Mech. 8 (1959), 77–94. MR 0102608
  • [3] Akira Koohara, Similarity principle of the generalized Cauchy-Riemann equations for several complex variables, J. Math. Soc. Japan 23 (1971), 213–249. MR 0374468,
  • [4] Akira Koohara, Representation of pseudo-holomorphic functions of several complex variables, J. Math. Soc. Japan 28 (1976), no. 2, 257–277. MR 0427673,
  • [5] Lê Hùng So’n, Fortsetzungssätze vom Hartogsschen Typ für verallgemeinerte analytische Funktionen mehrerer komplexer Variabler, Math. Nachr. 93 (1979), 177–186 (German). MR 579852,
  • [6] G. A. Magomedov and V. P. Paramodov, Generalized analytic functions of several variables, Math. USSR-Sb. 35 (1979), 181-205.
  • [7] L. G. Mihailov, On compatibility conditions and the manifold of solutions of the generalized Cauchy-Riemann system in several variables, Soviet Math. Dokl. 20 (1979), 1430-1435.
  • [8] W. Tutschke, Partielle komplexe Differentialgleichungen in einer und in mehreren komplexen Variablen, VEB Deutscher Verlag der Wissenschaften, Berlin, 1977 (German). Mit losen Berichtigungen; Hochschulbücher für Mathematik, Band 82. MR 0481388

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Keywords: Plentiful, pseudo-holomorphic function with characteristic, tangential
Article copyright: © Copyright 1982 American Mathematical Society

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