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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
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.

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  • [1] L. Hörmander, An introduction to complex analysis in several variables, Van Nostrand, Princeton, N. J., 1966. MR 34 #2933. MR 0203075 (34:2933)
  • [2] B. Malgrange, Ideals of differentiable functions, Tata Institute of Fundamental Research, Bombay and Oxford Univ. Press, London, 1967. MR 35 #3446. MR 0212575 (35:3446)

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

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