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


Integral representations and the complex Monge-Ampère equation in strictly convex domains

Author: Nancy K. Stanton
Journal: Proc. Amer. Math. Soc. 75 (1979), 276-278
MSC: Primary 32A25
MathSciNet review: 532150
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Abstract: We prove a relationship between Aizenberg's integral representation formula for holomorphic functions in a strictly convex domain and the complex Monge-Ampère equation.

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

  • [1] Patrick Ahern and Robert Schneider, The boundary behavior of Henkin’s kernel, Pacific J. Math. 66 (1976), no. 1, 9–14. MR 0435449 (55 #8409)
  • [2] L. A. Aizenberg, Integral representations of functions which are holomorphic in convex regions of $ {{\mathbf{C}}^n}$ space, Dokl. Akad. Nauk SSSR 151 (1963), 1247-1249; English, transl., Soviet Math. Dokl. 4 (1963), 1149-1152.
  • [3] Charles L. Fefferman, Monge-Ampère equations, the Bergman kernel, and geometry of pseudoconvex domains, Ann. of Math. (2) 103 (1976), no. 2, 395–416. MR 0407320 (53 #11097a)
  • [4] François Norguet, Introduction aux fonctions de plusieurs variables complexes: représentations intégrales, Fonctions de plusieurs variables complexes (Sém. François Norguet, 1970–1973; à la mémoire d’André Martineau), Springer, Berlin, 1974, pp. 1–97. Lecture Notes in Math., Vol. 409 (French). MR 0369729 (51 #5961)

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PII: S 0002-9939(1979)0532150-2
Article copyright: © Copyright 1979 American Mathematical Society

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