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Proceedings of the American Mathematical Society

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

 

 

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: 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?)

  • [1] Lars Hörmander, An introduction to complex analysis in several variables, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1966. MR 0203075
  • [2] 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

DOI: https://doi.org/10.1090/S0002-9939-1970-0261030-7
Keywords: Several complex variables, pseudo-convexity, Hartogs' Theorem, Whitney functions
Article copyright: © Copyright 1970 American Mathematical Society