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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Strict complex convexity
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by Robert Carmignani PDF
Proc. Amer. Math. Soc. 57 (1976), 285-290 Request permission

Abstract:

The strictly subharmonic and strictly plurisubharmonic functions are characterized using distribution theory, namely, the distributional Laplacian and the distributional complex Hessian. Then the analogous results for strictly convex functions are given.
References
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  • Lars Hörmander, Linear partial differential operators, Die Grundlehren der mathematischen Wissenschaften, Band 116, Springer-Verlag New York, Inc., New York, 1969. Third revised printing. MR 0248435
  • Laurent Schwartz, Théorie des distributions, Publications de l’Institut de Mathématique de l’Université de Strasbourg, IX-X, Hermann, Paris, 1966 (French). Nouvelle édition, entiérement corrigée, refondue et augmentée. MR 0209834
  • V. S. Vladimirov, Methods of the theory of functions of complex variables, “Nauka", Moscow, 1964; English transl., M.I.T. Press, Cambridge, Mass., 1966. MR 30 #2163; 34 #1551. P. Lelong, Plurisubharmonic functions and positive differential forms, Gordon and Breach, New York, 1969. MR 39 #4436.
  • J. J. Kohn and L. Nirenberg, A pseudo-convex domain not admitting a holomorphic support function, Math. Ann. 201 (1973), 265–268. MR 330513, DOI 10.1007/BF01428194
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 57 (1976), 285-290
  • MSC: Primary 32F05
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0409896-7
  • MathSciNet review: 0409896