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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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An extension of Hartogs’ theorem for domains whose boundary is not smooth


Author: David G. Schaeffer
Journal: Proc. Amer. Math. Soc. 25 (1970), 714-715
MSC: Primary 32.20
DOI: https://doi.org/10.1090/S0002-9939-1970-0261030-7
MathSciNet review: 0261030
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Abstract | References | Similar Articles | Additional Information

Abstract: In this note we obtain an extension of Hartogs’ theorem on analytic continuation inside a bounded domain in ${C^n}$ which requires no assumption on the smoothness of the boundary. The standard proof of Hartogs’ theorem applies with the minor change of using a Whitney function as the boundary data.


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

  • Lars Hörmander, An introduction to complex analysis in several variables, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1966. MR 0203075
  • B. Malgrange, Ideals of differentiable functions, Tata Institute of Fundamental Research Studies in Mathematics, No. 3, Tata Institute of Fundamental Research, Bombay; Oxford University Press, London, 1967. MR 0212575

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Additional Information

Keywords: Several complex variables, pseudo-convexity, Hartogs’ Theorem, Whitney functions
Article copyright: © Copyright 1970 American Mathematical Society