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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
DOI: https://doi.org/10.1090/S0002-9939-1979-0532150-2
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?)

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  • [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.
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  • [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

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DOI: https://doi.org/10.1090/S0002-9939-1979-0532150-2
Article copyright: © Copyright 1979 American Mathematical Society